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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 automorphism-invariant 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.
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Table of Contents
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Articles
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Gene Abrams and Benjamin Schoonmaker — Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups
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Adel Alahmadi, S. K. Jain and Surjeet Singh — Characterizations of Almost Injective Modules
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Pedro A. Guil Asensio and Ashish K. Srivastava — Automorphism-Invariant Modules
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Stephen M. Buckley — Distributive Algebras, Isoclinism, and Invariant Probabilities
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Stefan Catoiu — Ideals of the Enveloping Algebra $U(sl_3)$
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Seçil Çeken and Mustafa Alkan — On Second Submodules
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Steven Dougherty, Jon-Lark Kim and Patrick Solé — Open Problems in Coding Theory
-
Steven T. Dougherty — Foundations of Algebraic Coding Theory
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Steven T. Dougherty and Esengül Saltürk — Counting $\mathbb {Z}_2 \mathbb {Z}_4$-Additive Codes
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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 — Rad-Projective $\delta $-Covers
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Małgorzata Jastrzȩbska and Jan Krempa — On Lattices of Annihilators
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Pramod Kanwar, André Leroy and Jerzy Matczuk — Clean Elements in Polynomial Rings
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Christian Lomp — On the Semiprime Smash Product Question
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Jerzy Matczuk — Minimal Prime Ideals and Derivations
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Edgar Martínez-Moro and Steve Szabo — On Codes over Local Frobenius Non-Chain Rings of Order 16
-
E. R. Puczyłowski — On Quasi-Duo Rings
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Hamid Usefi — Isomorphism Invariants of Enveloping Algebras
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-
Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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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 automorphism-invariant 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 — Automorphism-Invariant 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, Jon-Lark 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 — Rad-Projective $\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 Martínez-Moro and Steve Szabo — On Codes over Local Frobenius Non-Chain Rings of Order 16
-
E. R. Puczyłowski — On Quasi-Duo Rings
-
Hamid Usefi — Isomorphism Invariants of Enveloping Algebras
