Noncommutative Rings and Their Applications

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.