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A Theory Of Non-Noetherian Gorenstein Rings, Livia M. Miller
A Theory Of Non-Noetherian Gorenstein Rings, Livia M. Miller
Department of Mathematics: Dissertations, Theses, and Student Research
In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay rings. Regular non-Noetherian rings were originally defined by Bertin in 1971. In 2007, Hamilton and Marley used Cech cohomology to introduce a theory of Cohen-Macaulay for non-Noetherian rings, answering a question posed by Glaz. This dissertation provides a theory of non-Noetherian Gorenstein rings agreeing with the Noetherian definition, and for which regular rings are Gorenstein, and coherent Gorenstein rings are Cohen-Macaulay. The relationship between Gorenstein rings and FP-injective dimension as defined by Stenstrom is also explored. Finally, an additional characterization of Gorenstein rings involving homological dimensions is examined …
Oscillation Theory Of Dynamic Equations On Time Scales, Raegan J. Higgins
Oscillation Theory Of Dynamic Equations On Time Scales, Raegan J. Higgins
Department of Mathematics: Dissertations, Theses, and Student Research
In past years mathematical models of natural occurrences were either entirely continuous or discrete. These models worked well for continuous behavior such as population growth and biological phenomena, and for discrete behavior such as applications of Newton's method and discretization of partial differential equations. However, these models are deficient when the behavior is sometimes continuous and sometimes discrete. The existence of both continuous and discrete behavior created the need for a different type of model. This is the concept behind dynamic equations on time scales. For example, dynamic equations can model insect populations that are continuous while in season, die …
C*-Extreme Points Of The Generalized State Space Of A Commutative C*-Algebra, Martha Gregg
C*-Extreme Points Of The Generalized State Space Of A Commutative C*-Algebra, Martha Gregg
Department of Mathematics: Dissertations, Theses, and Student Research
The generalized state space of a commutative C*-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. We show that a C*-extreme point of SH(C(X)) satisfies a certain spectral condition on the operators in the range of an associated measure, which is a positive operator-valued measure on …