Open Access. Powered by Scholars. Published by Universities.®

Algebra Commons

Open Access. Powered by Scholars. Published by Universities.®

1,266 Full-Text Articles 1,297 Authors 438,733 Downloads 131 Institutions

All Articles in Algebra

Faceted Search

1,266 full-text articles. Page 6 of 48.

Semi De Morgan Logic Properly Displayed, Giuseppe Greco, Fei Qin, M. Andrew Moshier, Alessandra Palmigiano 2020 Utrecht University

Semi De Morgan Logic Properly Displayed, Giuseppe Greco, Fei Qin, M. Andrew Moshier, Alessandra Palmigiano

Mathematics, Physics, and Computer Science Faculty Articles and Research

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.


A General Setting For Functions Of Fueter Variables: Differentiability, Rational Functions, Fock Module And Related Topics, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa 2020 Chapman University

A General Setting For Functions Of Fueter Variables: Differentiability, Rational Functions, Fock Module And Related Topics, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.


Locally Recoverable Codes From Planar Graphs, Kathryn Haymaker, Justin O'Pella 2020 Villanova University

Locally Recoverable Codes From Planar Graphs, Kathryn Haymaker, Justin O'Pella

Kanbar College Faculty Papers

In this paper we apply Kadhe and Calderbank’s definition of LRCs from convex polyhedra and planar graphs [4] to analyze the codes resulting from 3-connected regular and almost regular planar graphs. The resulting edge codes are locally recoverable with availability two. We prove that the minimum distance of planar graph LRCs is equal to the girth of the graph, and we also establish a new bound on the rate of planar graph edge codes. Constructions of regular and almost regular planar graphs are given, and their associated code parameters are determined. In certain cases, the code families meet the ...


A Proof Of A Hall-Littlewood Polynomial Formula, Jianbai Xu 2020 University of Windsor

A Proof Of A Hall-Littlewood Polynomial Formula, Jianbai Xu

Major Papers

This paper proves a Hall-Littlewood polynomial formula in a paper by Ram [Ram06] using a theorem by Schwer [Sch06]. We review materials relating to root systems, affine Weyl groups and ane Hecke algebras that are required to study alcoves, galleries and the Hall-Littlewood polynomials. In order to prove the Hall-Littlewood polynomial formula, we formulate in a special case Schwer's formula in Theorem 5.5 [Sch06] computing right multiplication of the alcove basis by standard basis elements. We show that Ram's formula for Hall-Littlewood polynomials in terms of positively folded alcove walks coincides with the formulation of Schwer's ...


Ziplines And Stuntwork, Kelly W. Remijan 2020 Illinois Mathematics and Science Academy

Ziplines And Stuntwork, Kelly W. Remijan

Teacher Resources

This activity involves an engineering activity which connects the work of stuntmen/stuntwomen working with ziplines to the concept of linear functions. Students create a physical model replicating a given situation and then model the zipline algebraically by writing the equation of the zipline.


Algebraic And Geometric Properties Of Hierarchical Models, Aida Maraj 2020 University of Kentucky

Algebraic And Geometric Properties Of Hierarchical Models, Aida Maraj

Theses and Dissertations--Mathematics

In this dissertation filtrations of ideals arising from hierarchical models in statistics related by a group action are are studied. These filtrations lead to ideals in polynomial rings in infinitely many variables, which require innovative tools. Regular languages and finite automata are used to prove and explicitly compute the rationality of some multivariate power series that record important quantitative information about the ideals. Some work regarding Markov bases for non-reducible models is shown, together with advances in the polyhedral geometry of binary hierarchical models.


An Elementary Treatise On The Application Of The Algebraic Analysis To Geometry, Wesley Stoker Barker Woolhouse 2020 Livre de Lyon

An Elementary Treatise On The Application Of The Algebraic Analysis To Geometry, Wesley Stoker Barker Woolhouse

Science and Mathematical Science

The decidedly great advantage of the Modern Mathematicians over the Ancients, has almost entirely a risen from the introduction and refinement of the Algebraic Analysis, united with the Differential and Integral Calculus; and particularly from the truly elegant and systematic mode which has been adopted in their application to problems connected with Geometry.


Geogebra Activities: Tracing Points, Jeremy Aikin, Corey Dunn, Jeffrey Meyer, Rolland Trapp 2020 CSUSB

Geogebra Activities: Tracing Points, Jeremy Aikin, Corey Dunn, Jeffrey Meyer, Rolland Trapp

Q2S Enhancing Pedagogy

In this activity, we will learn how to use GeoGebra (www.geogebra.org) to trace the movement of points, which depend on the movement of other objects. The paths of these points determine curves and we will provide algebraic descriptions of these curves.


Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache 2020 University of New Mexico

Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.


Introduction To Neutroalgebraic Structures And Antialgebraic Structures (Revisited), Florentin Smarandache 2020 University of New Mexico

Introduction To Neutroalgebraic Structures And Antialgebraic Structures (Revisited), Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined. Again, in all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations ...


An Invitation To Linear Algebra (2nd Edition), David N. Pham, Jonathon Funk, Wenjian Liu 2020 CUNY Queensborough Community College

An Invitation To Linear Algebra (2nd Edition), David N. Pham, Jonathon Funk, Wenjian Liu

Open Educational Resources

This is an OER textbook on linear algebra.


The Neutrosophic Triplet Of 𝑩𝑰-Algebras, Florentin Smarandache, Akbar Rezaei 2020 University of New Mexico

The Neutrosophic Triplet Of 𝑩𝑰-Algebras, Florentin Smarandache, Akbar Rezaei

Mathematics and Statistics Faculty and Staff Publications

In this paper, the concepts of a Neutro-𝐵𝐼-algebra and Anti-𝐵𝐼-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-𝐵𝐼-algebra is an alternative of the class of 𝐵𝐼-algebras.


Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi 2020 University of New Mexico

Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi

Mathematics and Statistics Faculty and Staff Publications

This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.


On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei 2020 University of New Mexico

On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei

Mathematics and Statistics Faculty and Staff Publications

In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.


New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal 2020 University of New Mexico

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the ...


Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache 2020 University of New Mexico

Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.


A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim 2020 University of New Mexico

A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim

Mathematics and Statistics Faculty and Staff Publications

In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CI-algebras are not BE-algebras.


Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache 2020 University of New Mexico

Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.


Connectedness In Cayley Graphs And P/Np Dichotomy For Quay Algebras, Thuy Trang Nguyen 2020 Bard College

Connectedness In Cayley Graphs And P/Np Dichotomy For Quay Algebras, Thuy Trang Nguyen

Senior Projects Spring 2020

This senior thesis attempts to determine the extent to which the P/NP dichotomy of finite algebras (as proven by Bulatov, et.al in 2017) can be cast in terms of connectedness in Cayley graphs. This research is motivated by Prof. Robert McGrail's work ``CSPs and Connectedness: P/NP-Complete Dichotomy for Idempotent, Right Quasigroups" published in 2014 in which he demonstrates the strong correspondence between tractability and total path-connectivity in Cayley graphs for right, idempotent quasigroups. In particular, we will introduce the notion of total V-connectedness and show how it could be potentially used to phrase the dichotomy in ...


N-Cycle Splines Over Sexy Rings, Jacob Tilden Cummings 2020 Bard College

N-Cycle Splines Over Sexy Rings, Jacob Tilden Cummings

Senior Projects Spring 2020

In this project we abstract the work of previous bard students by introducing the concept of splines over non-integers, non-euclidean domains, and even non-PIDs. We focus on n-cycles for some natural number n. We show that the concept of flow up class bases exist in PID splines the same way they do in integer splines, remarking the complications and intricacies that arise when abstracting from the integers to PIDs. We also start from scratch by finding a flow up class basis for n-cycle splines over the real numbers adjoin two indeterminates, denoted R[x,y] which necessitate more original techniques.


Digital Commons powered by bepress