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.
Leavitt path algebras of Cayley graphs arising from cyclic groups by G.
Abrams and B. Schoonmaker
Characterizations of almost injective modules by A. Alahmadi, S. K. Jain, and
S. Singh
Automorphism-invariant modules by P. A. Guil Asensio and A. K. Srivastava
Distributive algebras, isoclinism, and invariant probabilities by S. M.
Buckley
Ideals of the enveloping algebra $U(sl_3)$ by S. Catoiu
On second submodules by S. Ceken and M. Alkan
Open problems in coding theory by S. T. Dougherty, J.-L. Kim, and P. Sole
Foundations of algebraic coding theory by S. T. Dougherty
Counting $\mathbb{Z}_2\mathbb{Z}_4$-additive codes by S. T. Dougherty and E.
Salturk
From endomorphism rings to some noteworthy ideals in categories of modules by
A. Facchini
Lie and Jordan properties in group algebras by E. G. Goodaire and C. P.
Milies
Rad-projective $\delta$-covers by Y. Ibrahim and M. Yousif
On lattices of annihilators by M. Jastrzebska and J. Krempa
Clean elements in polynomial rings by P. Kanwar, A. Leroy, and J. Matczuk
On the semiprime smash product question by C. Lomp
Minimal prime ideals and derivations by J. Matczuk
On codes over local Frobenius non-chain rings of order 16 by E. Martinez-Moro
and S. Szabo
On quasi-duo rings by E. R. Puczylowski
Isomorphism invariants of enveloping algebras by H. Usefi
Steven Dougherty, University of Scranton, PA, USA.
Alberto Facchini, Universita di Padova, Italy.
Andre Leroy, Universite d'Artois, Lens, France.
Edmund Puczylowski, University of Warsaw, Poland.
Patrick Sole, CNRS/LTCI, Telecom ParisTech, France.
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