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The Effects Of Analytic Reading Skills On Sixth Graders' Ability To Solve Mathematical Story Problems., Linda Hale Eilers
The Effects Of Analytic Reading Skills On Sixth Graders' Ability To Solve Mathematical Story Problems., Linda Hale Eilers
LSU Historical Dissertations and Theses
The purpose of the present study was to determine the effects of two levels of instructional treatment on sixth graders' ability to solve mathematical story problems. The two levels of instructional treatment were instruction in the use of graphic organizers in conjunction with specific analytic reading skills and instruction in specific analytic reading instruction alone. These were compared to the absence of either treatment. The steady decline in students' scores on measures of ability to read and solve story problems over the past decade prompted research in three sixth-grade public school classes in northeast Louisiana. The study employed an experimental/control, …
On The Homology Of Branched Cyclic Covers Of Knots., Wayne H. Stevens
On The Homology Of Branched Cyclic Covers Of Knots., Wayne H. Stevens
LSU Historical Dissertations and Theses
We consider the sequence of finite branched cyclic covers of $S\sp3$ branched along a tame knot $K : S\sp1\to S\sp3$ and prove several results about the homology of these manifolds. We show that the sequence of cyclic resultants of the Alexander polynomial of K satisfies a linear recursion formula with integral coefficients. This means that the orders of the first homology groups of the branched cyclic covers of K can be computed recursively. We further establish the existence of a recursion formula that generates sequences which contain the square roots of the orders of the odd-fold covers and that contain …
Existence And Uniqueness Theorems For Some White Noise Integral Equations., Dongya Zou
Existence And Uniqueness Theorems For Some White Noise Integral Equations., Dongya Zou
LSU Historical Dissertations and Theses
Let $({\cal S})\sbsp{\beta}{*},0\le\beta<1,$ be the Kondratiev-Streit spaces of generalized functions. Let $f:\lbrack 0,T\rbrack\times ({\cal S})\sbsp{\beta}{*}\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable, and satisfy a growth condition and a Lipschitz condition. Let $\theta :\lbrack 0, T\rbrack\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable and satisfy a growth condition. Then it is shown that the white noise integral equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}f(s, X\sb{s})ds,0\le t\le T,$ has a unique solution in $({\cal S})\sbsp{\beta}{*}$, where the integral is a white noise integral in the Pettis or Bochner sense. This result is extended to ${\cal M}\sp*$, the Meyer-Yan distribution space. Some special equations are also solved explicitly. For $F\in L\sp2({\bf R}\sp+)$, let $A\sb{s}=\int\sbsp{-\infty}{s} F(s-u)\partial\sb{u}du,\ E\sb{s}= {\rm exp}(A\sb{s}),$ and $A\sbsp{s}{*},\ E\sbsp{s}{*}$ be their duals, respectively. The equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} A\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is solved in $({\cal S})\sp*$ or $(L\sp2)$, and the equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} E\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0, T\rbrack,$ is solved in ${\cal M}\sp*,$ where $\theta$ is as above. Moreover, under certain conditions on $\theta,\Phi:\lbrack 0,T\rbrack\to ({\cal S})\sp*$ and $\sigma:\lbrack 0,T\rbrack\sp2\to{\bf R},$ the Volterra equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}\sigma(t,s)\Phi\sb{s}\ {\rm o}\ X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is also solved, and its solution is in ${\cal M}\sp*, ({\cal S})\sbsp{\beta}{*},$ or $(L\sp2),$ depending on the growth conditions for $\theta$ and $\Phi.$ Finally, for a suitable deterministic function f, the white noise partial differential equation ${\partial u\over\partial t}=\Delta u+:e\sp{\dot B\sb{x}}: {\rm o}\thinspace u, u(0,x)=f(x),x\in{\bf R}\sp{n}, t\in\lbrack 0,\infty),$ is solved in ${\cal M}\sp*$.
Szasz-Muntz Theorems For Nilpotent Lie Groups., Darwyn C. Cook
Szasz-Muntz Theorems For Nilpotent Lie Groups., Darwyn C. Cook
LSU Historical Dissertations and Theses
The classical Szasz-Muntz theorem says that for $f\ \in\ L\sp2(\lbrack 0, 1\rbrack )$ and $\{n\sb{k}\}\sbsp{k=1}{\infty}$ a strictly increasing sequence of positive integers,$$\int\limits\sbsp{0}{1}x\sp{n\sb{j}}f(x)dx=0\ \forall j\Rightarrow f=0\Leftrightarrow\sum\sbsp{j=1}{\infty}{{1}\over{n\sb{j}}}=\infty.$$We have generalized this theorem to compactly supported functions on $\Re\sp{n}$ and to an interesting class of nilpotent Lie groups. On $\Re\sp{n}$ we rephrased the condition above on an integral against a monomial as a condition on the derivative of the Fourier transform $\ f$. For compactly supported f this transform has an entire extension to complex n-space, and these derivatives are coefficients in a Taylor series expansion of $\ f$. In the nilpotent Lie groups …
Some Lifting Problems In Arithmetic Equivalence., Nancy C. Colwell
Some Lifting Problems In Arithmetic Equivalence., Nancy C. Colwell
LSU Historical Dissertations and Theses
The main theorem in this dissertation provides a partial answer to the following question: Given a $\doubz\sb{p}$-extension $F{\sb\infty} /F$ and a finite extension $K/F$, where F is a number field and p a prime number, to what extent does the K-splitting behavior the prime ideals of F determine the Iwasawa invariants of the $\doubz\sb{p}$-extension $K{\cdot}F{\sb\infty}/K$. The answer is that if two fields K and L are arithmetically equivalent over F, then $K{\cdot}F{\sb\infty} /K$ and $L{\cdot}F{\sb\infty} /L$ have exactly the same Iwasawa invariants for any $\doubz\sb{p}$-extension $F{\sb\infty} /F$, so long as p is not an exceptional divisor for K and L …
The Generalized Kompaneets Equation., Kunyang Wang
The Generalized Kompaneets Equation., Kunyang Wang
LSU Historical Dissertations and Theses
In the dissertation, the generalized Kompaneets equation$${\partial u\over\partial t}={1\over\beta(x)}\lbrack\alpha(x)(u\sb{x}+ku+F(x,u))\rbrack\sb{x}$$(for $x,t>0)$ is studied. For the linear case, when $F\equiv0,$ a complete theory is given. A brief discussion is carried for the nonlinear case when $F(x,u)=f(x)g(u).$. For the following equation,$$v\sb{t}=\varphi(y,v\sb{y})v\sb{yy}+\psi(y,v,v\sb{y}),$$Goldstein and Lin's result is extended to degenerate case. Also, for the following linear operator,$$Au=\alpha(x)u\prime\prime+\beta(x)u\prime$$(for $x\in \lbrack 0,$ 1)), Clement and Timmermans' result is extended to the case of discontinuous coefficients $\alpha$ and $\beta$.
A Polynomial Invariant Of Links In A Solid Torus., Jaehoo Park Kim
A Polynomial Invariant Of Links In A Solid Torus., Jaehoo Park Kim
LSU Historical Dissertations and Theses
A polynomial invariant of links in a solid torus is defined through an algebra $H\sb{n}({1\over2}$). $H\sb{n}({1\over2}$) modulo by an ideal is the type-B Hecke algebra. This invariant satisfies the $S\sb3$-skein relation as in the 1-trivial links case of dicromatic link invariant discovered by J. Hoste and M. Kidwell. A link in the solid torus is isotopic to a closed braid which is a braid in the braid group of the annulus. We find an invariant of links through a represention $\pi$ of the braid group of the annulus to the algebra $H\sb{n}({1\over2}$). A trace map X is defined on a …
Jordan Algebras And Lie Semigroups., Yongdo Lim
Jordan Algebras And Lie Semigroups., Yongdo Lim
LSU Historical Dissertations and Theses
For a Euclidean Jordan algebra V with the corresponding symmetric cone $\Omega$, we consider the semigroup $\Gamma\sb{\Omega}$ of elements in the automorphism group $G(T\sb{\Omega})$ of the tube domain $V$ + $i\Omega$ which can be extended to $\Omega$ and maps $\Omega$ into itself. A study of this semigroup was first worked out by Koufany in connection to Jordan algebra theory and Lie theory of semigroups. In this work we give a new proof of Koufany's results and generalize up to infinite dimensional Jordan algebras, so called $JB$-algebras. One of the nice examples of the semigroup $\Gamma\sb{\Omega}$ is from the Jordan algebra …
Matroid Connectivity., John Leo
Matroid Connectivity., John Leo
LSU Historical Dissertations and Theses
This dissertation has three parts. The first part, Chapter 1, considers the coefficient $b\sb{ij}(M)$ of $x\sp{i}y\sp{j}$ in the Tutte polynomial of a connected matroid M. The main result characterizes, for each i and j, the minor-minimal such matroids for which $b\sb{ij}(M)>0.$ One consequence of this characterization is that $b\sb{11}(M)>0$ if and only if the two-wheel is a minor of M. Similar results are obtained for other values of i and j. These results imply that if M is simple and representable over $GF(q),$ then there are coefficients of its Tutte polynomial which count the flats of M that …
On The Relationship Between Representation Equivalence And Isomorphism Of Fundamental Groups Of Three-Step Nilmanifolds., Colathur Raja Vijayan
On The Relationship Between Representation Equivalence And Isomorphism Of Fundamental Groups Of Three-Step Nilmanifolds., Colathur Raja Vijayan
LSU Historical Dissertations and Theses
This dissertation arose from efforts to investigate an example which appeared in (G) of a phenomenon which has been considered to be rare: namely, the existence of two discrete cocompact subgroups $\Gamma\sb1$ and $\Gamma\sb2$ in a Lie group G such that $\Gamma\sb1/G$ and $\Gamma\sb2/G$ have the same (unitary) spectrum but $\Gamma\sb1$ is not isomorphic to $\Gamma\sb2.$ This phenomenon may be called representation equivalence of $\Gamma\sb1$ and $\Gamma\sb2$ with $\Gamma\sb1$ non-isomorphic to $\Gamma\sb2.$. In (G) the first known example of this phenomenon in the class of solvable Lie groups was given. In this example G was a specific three-step nilpotent Lie …
Continuously Differentiable Selections And Parametrizations Of Multifunctions In One Dimension., Craig Knuckles
Continuously Differentiable Selections And Parametrizations Of Multifunctions In One Dimension., Craig Knuckles
LSU Historical Dissertations and Theses
Sufficient conditions are given for a multifunction (set-valued function) to admit a continuously differentiable selection in one dimension. These conditions are given in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction. Also, the multifunctions in one dimension that can be parametrized with continuously differentiable functions are completely characterized. The characterization is again in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction.
Link Theory: Applications To Real Algebraic Curves., Stephen Patrick Paris
Link Theory: Applications To Real Algebraic Curves., Stephen Patrick Paris
LSU Historical Dissertations and Theses
Hilbert in his sixteenth problem asks us to study the topology of real algebraic varieties. There are many equalities, inequalities, and congruences associated to a real algebraic curve. Extremal properties have been derived for many of the inequalities. In 1980, V. A. Rokhlin derived two inequalities associated to a real algebraic curve. In this dissertation we use methods developed by P. Gilmer to rederive Rokhlin's inequalities. Using these methods we then derive an extremal property for one of the inequalities. Although this extremal property was not studied by Rokhlin, we also show that Rokhlin's ideas can be utilized to prove …
Abstract Volterra Equations., Mihi Kim
Abstract Volterra Equations., Mihi Kim
LSU Historical Dissertations and Theses
This dissertation is devoted to the study of the abstract Volterra equation $$v(t) = A\int\sbsp{0}{t}\ v(t - s)d\mu(s) + f(t)\qquad{\rm for}\ t\ge0,\eqno&(\rm VE)$$. where A is a closed linear operator in a complex Banach space $X,\ \mu$ is a complex valued function of local bounded variation, and $f:\lbrack0,\infty)\to X$ is continuous and Laplace transformable. Laplace transform methods are used to characterize the existence and uniqueness of exponentially bounded solutions v for a given forcing term f, an operator A, and a given kernel $\mu$. We extend the methods of a solution family (or a resolvent) for (VE) by studying integrated …
The Determination Of A Matroid's Structure From Properties Of Certain Large Minors., Allan Donald Mills
The Determination Of A Matroid's Structure From Properties Of Certain Large Minors., Allan Donald Mills
LSU Historical Dissertations and Theses
This dissertation solves some problems related to the structure of matroids. In Chapter 2, we prove that if M and N are distinct connected matroids on a common ground set E, where $\vert E\vert \ge 2,$ and, for every e in $E,\ M\\ e = N\\ e$ or M/e = N/e, then one of M and N is a relaxation of the other. In addition, we determine the matroids M and N on a common ground set E such that, for every pair of elements $\{ e,f\}$ of E, at least two of the four corresponding minors of M and …
Some Problems In Algebraic And Extremal Graph Theory., Edward Tauscher Dobson
Some Problems In Algebraic And Extremal Graph Theory., Edward Tauscher Dobson
LSU Historical Dissertations and Theses
In this dissertation, we consider a wide range of problems in algebraic and extremal graph theory. In extremal graph theory, we will prove that the Tree Packing Conjecture is true for all sequences of trees that are 'almost stars'; and we prove that the Erdos-Sos conjecture is true for all graphs G with girth at least 5. We also conjecture that every graph G with minimal degree k and girth at least $2t+1$ contains every tree T of order $kt+1$ such that $\Delta(T)\leq k.$ This conjecture is trivially true for t = 1. We Prove the conjecture is true for …
On Some Problems In The Algebraic Theory Of Quadratic Forms., Hamza Y. Ahmad
On Some Problems In The Algebraic Theory Of Quadratic Forms., Hamza Y. Ahmad
LSU Historical Dissertations and Theses
This work consists of results on three questions in the algebraic theory of forms. The first question deals with characterizing the Witt kernel (i.e. the anisotropic non-singular quadratic forms over that become hyperbolic) over a given field extension. For separable quadratic and bi-quadratic extension this is well known (for example see (B1, 4.2 and 4.3), (B2, p. 121), (L, p. 200), (ELW, 2.12)). In chapter 2, we provide answers to this question for inseparable quadratic and bi-quadratic extensions. We provide theorem 2.1.5, which in particular answers question 4.4 in (B2). From this result we prove the excellence property for inseparable …
Modules Associated To Disconnected Surfaces By Quantization Functors., Basinyi Chimitza
Modules Associated To Disconnected Surfaces By Quantization Functors., Basinyi Chimitza
LSU Historical Dissertations and Theses
Blanchet, Habegger, Masbaum and Vogel defined a quantization functor on a category whose objects are oriented closed surfaces together with a collection of colored banded points and $p\sb1$-structure. The functor assigns a module $V\sb{p}(\Sigma)$ to each surface $\Sigma$. This assignment satisfies certain axioms. For p even, it satisfies the tensor product axiom, which gives the modules associated to a disconnected surface as the tensor-product of the modules associated to its components. In this dissertation we show that the p odd case satisfies a generalized tensor product formula. The notion of a generalized tensor product formula is due to Blanchet, and …
Counting On You: The Rhetoric Of The National Council Of Teachers Of Mathematics "Standards"., Michael R. Dreher
Counting On You: The Rhetoric Of The National Council Of Teachers Of Mathematics "Standards"., Michael R. Dreher
LSU Historical Dissertations and Theses
This study sought to initiate the process of identifying the rhetoric of mathematics as a distinct field of research, while acknowledging its basis in the rhetoric of science and other literatures. Accordingly, the study started by examining the external basis of the rhetoric of mathematics; in other words, how discourse affects the way in which the culture views mathematics. The primary text for this study was the National Council of Teachers of Mathematics' three-volume Standards for School Mathematics. This document, designed to reform mathematics education from kindergarten through twelfth grade, was shown not to be completely successful in its goal …
Multiplicities And Transforms Of Ideals., Juan Antonio Nido Valencia
Multiplicities And Transforms Of Ideals., Juan Antonio Nido Valencia
LSU Historical Dissertations and Theses
Let (R, M$\sb{\rm R})$ be a regular local ring of dimension 3 of the form k (x,y,z) $\sb{\rm (x,y,z)},$ where k is an algebraically closed field and let I be an M$\sb{\rm R}$-primary ideal that admits generators. We prove that if I$\sb1$ is the proper transform of I to a quadratic transform (A, M$\sb{\rm A})$ of(R, M$\sb{\rm R})$ such that the analytic spread of I$\sb1$ is 3 and the generators of I$\sb1$ induced by those of I satisfy certain divisibility conditions, then the inequality of multiplicities$$\rm e\sb{A}(M(I\sb1)) < e\sb{R}(I)$$is valid, where M $\rm(I\sb1) \supseteq I\sb1$ is an M$\sb{\rm A}$-primary ideal associated to I$\sb1$ (the ideal I$\sb1$ may not be M$\sb{\rm A}$-primary if dim (R) = 3) through an operation M that we define for ideals in a regular local ring.
Locally Generated Semigroups., Genaro Segundo Gonzalez
Locally Generated Semigroups., Genaro Segundo Gonzalez
LSU Historical Dissertations and Theses
For a topological semigroup S, Lawson constructed a semigroup $\Gamma(S)$ with the property that any local homomorphism defined in a neighborhood of the identity of S to a topological semigroup T extends uniquely to a global homomorphism defined on $\Gamma(S).$ In this work we obtain conditions on S to topologize the semigroup $\Gamma(S)$ via an uniformity such that the extended homomorphism is continuous and such that $\Gamma(S)$ is a topological semigroup. We also investigate a different approach of the problem via the relatively free semigroup RF(U) where U is a suitable neighborhood of the identity of S and show that …
A Paley-Wiener Theorem For All Two And Three-Step Nilpotent Lie Groups., Robert Reeve Park
A Paley-Wiener Theorem For All Two And Three-Step Nilpotent Lie Groups., Robert Reeve Park
LSU Historical Dissertations and Theses
A Paley-Wiener Theorem for all connected, simply-connected two and three-step nilpotent Lie groups is proved. If f $\epsilon \ L\sbsp{c}{\infty}({G}),$ where G is a connected, simply-connected two or three-step nilpotent Lie group such that the operator-valued Fourier transform $\\varphi(\pi)$ = 0 for all $\pi$ in E, a subset of G of positive Plancherel measure, then it is shown that f = 0 a. e. on G. The proof uses representation-theoretic methods from Kirillov theory for nilpotent Lie groups, and uses an integral formula for the operator-valued Fourier transform $\\varphi(\pi)$. It is also shown by example that the condition that G …
Structural Results For Matroids., Sandra Reuben Kingan
Structural Results For Matroids., Sandra Reuben Kingan
LSU Historical Dissertations and Theses
This dissertation solves some problems involving the structure of matroids. In Chapter 2, the class of binary matroids with no minors isomorphic to the prism graph, its dual, and the binary affine cube is completely determined. This class contains the infinite family of matroids obtained by sticking together a wheel and the Fano matroid across a triangle, and then deleting an edge of the triangle. In Chapter 3, we extend a graph result by D. W. Hall to matroids. Hall proved that if a simple, 3-connected graph has a $K\sb5$-minor, then it must also have a $K\sb{3,3}$-minor, the only exception …
Graphs In Number Theory., Leigh Ann Myers
Graphs In Number Theory., Leigh Ann Myers
LSU Historical Dissertations and Theses
In the 1930's L. Redei and H. Reichardt established methods for determining the 4-rank of the narrow ideal class group of a quadratic number field, Q($D\sp{1/2}).$ One of these methods involves determining the number of D-splittings of the discriminant, D, of the number field. Later, this method was revised so that we need only find the rank of a matrix over F$\sb2$. In some cases, these Redei matrices can be viewed as adjacency matrices of graphs or digraphs. In Chapter I we introduce the graphs and matrices mentioned above, the method for finding 4-ranks, and present some preliminary results on …
The Generalized Distributive Law As Tacit Knowledge In Algebra., Juanita Lavall Bates
The Generalized Distributive Law As Tacit Knowledge In Algebra., Juanita Lavall Bates
LSU Historical Dissertations and Theses
The purposes of this study were to investigate theories that explain why common errors of the type ($a \pm b)\sp{c} = a\sp{c} \pm b\sp{c}$ and $\root c \of {a \pm b} = \root c \of {a} \pm \root c \of {b}$ occur in algebra problem solving by novices; and to develop and assess techniques for remediating these errors. The meaning theory of learning (ML), procedural learning theory (PL), and implicit structure learning theory (ISL) are alternative frameworks for the explanation of the errors. The ML theory hypothesizes that experts have rich semantic connections to the procedures and symbols of algebra, …
Generalizations Of The Optimal Control Problem For The Vidale-Wolfe Advertising Model., Richard Dale Edie
Generalizations Of The Optimal Control Problem For The Vidale-Wolfe Advertising Model., Richard Dale Edie
LSU Historical Dissertations and Theses
The purpose of this dissertation is to study two different generalizations of the optimal control problem based on the Vidale-Wolfe Advertising Model. The first problem is an infinite horizon free endpoint one-dimensional version of the Vidale-Wolfe optimal control problem of advertising in time varying markets. A solution is obtained for this problem. Then a thorough proof using the method of dynamic programming is presented to verify that this solution is optimal under reasonable market conditions. The second problem is a finite time fixed endpoint two-dimensional version of the Vidale-Wolfe optimal control problem. Normal optimal trajectories are obtained for this problem. …
On The Characterization Of Finite Dimensional Hida Distributions., Kyoung Sim Lee
On The Characterization Of Finite Dimensional Hida Distributions., Kyoung Sim Lee
LSU Historical Dissertations and Theses
The mathematical framework of white noise analysis is based on an infinite dimensional analogue of the Schwartz distribution theory. The Lebesgue measure on $\IR\sp{k}$ is replaced with standard Gaussian measures $\mu$ on infinite dimensional spaces. There is an infinite dimensional analogue $({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*$ of a Gel'fand triple ${\cal E}\subset E\subset{\cal E}\sp*$ which is obtained from ${\cal S}(\IR\sp{k})\subset L\sp2(\IR\sp{k})\subset{\cal S}\sp*(\IR\sp{k})$ in a general setup. There are spaces $({\cal E}\sp\beta),({\cal E}\sp\beta)\sp*, \beta\in\lbrack 0,1)$ with $({\cal E}\sp\beta)\subset({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*\subset({\cal E}\sp\beta)\sp*.$. The compositions of Schwartz distributions and Gaussian random variables have been discussed. A new Gel'fand triple ${\cal H}(\IR\sp{k})\subset{\cal …
Split Abelian Extensions Of Calgebras., Mark Andrew Curole
Split Abelian Extensions Of Calgebras., Mark Andrew Curole
LSU Historical Dissertations and Theses
It is shown that the C* algebra of a groupoid with Haar system has a natural split abelian extension. For a split abelian extension of a C* algebra it is shown that all representations of the original algebra extend to the split abelian extension. Under a reasonable assumption it is shown that states extend to a split abelian extension. Definitions for quasi-invariant and ergodic measures are given for split abelian extension of C* algebras, and it is shown when the split abelian extension is the natural extension of the C* algebra of a groupoid with Haar system that these definitions …
Linkage By Generically Gorenstein Cohen-Macaulay Ideals., Heath Mayall Martin
Linkage By Generically Gorenstein Cohen-Macaulay Ideals., Heath Mayall Martin
LSU Historical Dissertations and Theses
In a Gorenstein local ring R, two ideals A and B are said to be linked by an ideal I if the two relations A = (I: B) and B = (I: A) hold. In the case that I is a complete intersection, or a Gorenstein ideal, it is known that linkage preserves the Cohen-Macaulay property. That is, if A is a Cohen-Macaulay ideal, then so is B. However, if I is allowed to be a generically Gorenstein, Cohen-Macaulay ideal, easy examples show that this type of linkage does not preserve the Cohen-Macaulay property. The primary purpose of this work …
The Congruence Extension Property, The Ideal Extension Property, And Ideal Semigroups., Karen Dommert Aucoin
The Congruence Extension Property, The Ideal Extension Property, And Ideal Semigroups., Karen Dommert Aucoin
LSU Historical Dissertations and Theses
A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup of S extends to a congruence on S. The ideal extension property (IEP) for semigroups is defined analogously. A characterization of commutative semigroups with IEP is given in terms of multiplicative conditions within and between the archimedean components of the semigroup. A similar characterization of commutative semigroups with CEP is sought. Toward this end, archimedean semigroups with CEP are characterized in terms of multiplicative structure and a number of necessary conditions on multiplication between the archimedean components of a commutative semigroup with CEP are established. …
The Congruence Extension Property And Related Topics In Semigroups., Jill Ann Dumesnil
The Congruence Extension Property And Related Topics In Semigroups., Jill Ann Dumesnil
LSU Historical Dissertations and Theses
A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup can be extended to a congruence on the semi-group. This property, the ideal extension property (IEP), and other related concepts are studied from both an algebraic and a topological perspective in this work. A characterization of semigroups with CEP is given in terms of the lattice of congruences. A similar result is obtained for IEP. Semigroups in which the relation "is an ideal of" is transitive (t-semigroups) are explored. It is shown that each of CEP and IEP implies this condition and that these are …