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Softcover ISBN:  9781470410322 
Product Code:  CONM/634 
List Price:  $130.00 
MAA Member Price:  $117.00 
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AMS Member Price:  $100.00 
Softcover ISBN:  9781470410322 
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Book DetailsContemporary MathematicsVolume: 634; 2015; 265 ppMSC: Primary 16; 17; 94
This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1–4, 2013, at the Université d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.
Material from the course “Foundations of Algebraic Coding Theory“, given by Steven Dougherty, is included and provides the reader with the history and background of coding theory as well as the interplay between coding theory and algebra. In module theory, many new results related to (almost) injective modules, injective hulls and automorphisminvariant modules are presented. Broad generalizations of classical projective covers are studied and category theory is used to describe the structure of some modules. In some papers related to more classical ring theory such as quasi duo rings or clean elements, new points of view on classical conjectures and standard open problems are given. Descriptions of codes over local commutative Frobenius rings are discussed, and a list of open problems in coding theory is presented within their context.
ReadershipGraduate students and research mathematicians interested in noncommutative rings and coding theory.

Table of Contents

Articles

Gene Abrams and Benjamin Schoonmaker — Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups

Adel Alahmadi, S. K. Jain and Surjeet Singh — Characterizations of Almost Injective Modules

Pedro A. Guil Asensio and Ashish K. Srivastava — AutomorphismInvariant Modules

Stephen M. Buckley — Distributive Algebras, Isoclinism, and Invariant Probabilities

Stefan Catoiu — Ideals of the Enveloping Algebra $U(sl_3)$

Seçil Çeken and Mustafa Alkan — On Second Submodules

Steven Dougherty, JonLark Kim and Patrick Solé — Open Problems in Coding Theory

Steven T. Dougherty — Foundations of Algebraic Coding Theory

Steven T. Dougherty and Esengül Saltürk — Counting $\mathbb {Z}_2 \mathbb {Z}_4$Additive Codes

Alberto Facchini — From Endomorphism Rings to Some Noteworthy Ideals in Categories of Modules

Edgar G. Goodaire and César Polcino Milies — Lie and Jordan Properties in Group Algebras

Yasser Ibrahim and Mohamed Yousif — RadProjective $\delta $Covers

Małgorzata Jastrzȩbska and Jan Krempa — On Lattices of Annihilators

Pramod Kanwar, André Leroy and Jerzy Matczuk — Clean Elements in Polynomial Rings

Christian Lomp — On the Semiprime Smash Product Question

Jerzy Matczuk — Minimal Prime Ideals and Derivations

Edgar MartínezMoro and Steve Szabo — On Codes over Local Frobenius NonChain Rings of Order 16

E. R. Puczyłowski — On QuasiDuo Rings

Hamid Usefi — Isomorphism Invariants of Enveloping Algebras


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This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1–4, 2013, at the Université d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.
Material from the course “Foundations of Algebraic Coding Theory“, given by Steven Dougherty, is included and provides the reader with the history and background of coding theory as well as the interplay between coding theory and algebra. In module theory, many new results related to (almost) injective modules, injective hulls and automorphisminvariant modules are presented. Broad generalizations of classical projective covers are studied and category theory is used to describe the structure of some modules. In some papers related to more classical ring theory such as quasi duo rings or clean elements, new points of view on classical conjectures and standard open problems are given. Descriptions of codes over local commutative Frobenius rings are discussed, and a list of open problems in coding theory is presented within their context.
Graduate students and research mathematicians interested in noncommutative rings and coding theory.

Articles

Gene Abrams and Benjamin Schoonmaker — Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups

Adel Alahmadi, S. K. Jain and Surjeet Singh — Characterizations of Almost Injective Modules

Pedro A. Guil Asensio and Ashish K. Srivastava — AutomorphismInvariant Modules

Stephen M. Buckley — Distributive Algebras, Isoclinism, and Invariant Probabilities

Stefan Catoiu — Ideals of the Enveloping Algebra $U(sl_3)$

Seçil Çeken and Mustafa Alkan — On Second Submodules

Steven Dougherty, JonLark Kim and Patrick Solé — Open Problems in Coding Theory

Steven T. Dougherty — Foundations of Algebraic Coding Theory

Steven T. Dougherty and Esengül Saltürk — Counting $\mathbb {Z}_2 \mathbb {Z}_4$Additive Codes

Alberto Facchini — From Endomorphism Rings to Some Noteworthy Ideals in Categories of Modules

Edgar G. Goodaire and César Polcino Milies — Lie and Jordan Properties in Group Algebras

Yasser Ibrahim and Mohamed Yousif — RadProjective $\delta $Covers

Małgorzata Jastrzȩbska and Jan Krempa — On Lattices of Annihilators

Pramod Kanwar, André Leroy and Jerzy Matczuk — Clean Elements in Polynomial Rings

Christian Lomp — On the Semiprime Smash Product Question

Jerzy Matczuk — Minimal Prime Ideals and Derivations

Edgar MartínezMoro and Steve Szabo — On Codes over Local Frobenius NonChain Rings of Order 16

E. R. Puczyłowski — On QuasiDuo Rings

Hamid Usefi — Isomorphism Invariants of Enveloping Algebras