Noncommutative rings and their applications / I [edited by] Steven Dougherty...[et al.].

Includes bibliographical references.

Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups / Gene Abrams and Benjamin Schoonmaker --
Characterizations of Almost Injective Modules / Adel Alahmadi, S. K. Jain and Surjeet Singh --
Automorphism-Invariant Modules / Pedro A. Guil Asensio and Ashish K. Srivastava --
Distributive Algebras, Isoclinism, and Invariant Probabilities / Stephen M. Buckley --
Ideals of the Enveloping Algebra $U(sl_3)$ / Stefan Catoiu --
On Second Submodules / Seçil Çeken and Mustafa Alkan --
Open Problems in Coding Theory / Steven Dougherty, Jon-Lark Kim and Patrick Solé --
Foundations of Algebraic Coding Theory / Steven T. Dougherty --
Counting $\mathbb {Z}_2 \mathbb {Z}_4$-Additive Codes / Steven T. Dougherty and Esengül Saltürk --
From Endomorphism Rings to Some Noteworthy Ideals in Categories of Modules / Alberto Facchini --
Lie and Jordan Properties in Group Algebras / Edgar G. Goodaire and César Polcino Milies --
Rad-Projective $\delta $-Covers / Yasser Ibrahim and Mohamed Yousif --
On Lattices of Annihilators / Małgorzata Jastrzȩbska and Jan Krempa --
Clean Elements in Polynomial Rings / Pramod Kanwar, André Leroy and Jerzy Matczuk --
On the Semiprime Smash Product Question / Christian Lomp --
Minimal Prime Ideals and Derivations / Jerzy Matczuk --
On Codes over Local Frobenius Non-Chain Rings of Order 16 / Edgar Martínez-Moro and Steve Szabo --
On Quasi-Duo Rings / E. R. Puczyłowski --
Isomorphism Invariants of Enveloping Algebras / Hamid Usefi --

This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite 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.