Noncommutative rings and their applications : International Conference on Noncommutative Rings and Their Applications, July 1-4, 2013, Université d'Artois, Lens, France

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 appli...

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Bibliographic Details
Main Authors: Noncommutative Rings and Their Applications (Conference), Dougherty, Steven, Facchini, Alberto, Leroy, Andre (Andre Gerard), Puczylowski, Edmund, Sole, Patrick
Format: eBook Book
Language:English
Published: Providence, R.I American Mathematical Society 2015
Series:Contemporary mathematics
Subjects:
Associative rings and algebras > Chain conditions, growth conditions, and other forms of finiteness > Chain conditions on annihilators and summands: Goldie-type conditions. msc
Associative rings and algebras > Conditions on elements > None of the above, but in this section. msc
Associative rings and algebras > Radicals and radical properties of rings > Prime and semiprime rings. msc
Associative rings and algebras > Rings and algebras arising under various constructions > Group rings. msc
Associative rings and algebras > Rings and algebras arising under various constructions > None of the above, but in this section. msc
Information and communication, circuits > Theory of error-correcting codes and error-detecting codes > Cyclic codes. msc
Information and communication, circuits > Theory of error-correcting codes and error-detecting codes > Linear codes, general. msc
Information and communication, circuits > Theory of error-correcting codes and error-detecting codes > Other types of codes. msc
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Universal enveloping (super)algebras. msc
Noncommutative rings
Noncommutative rings > Congresses
Rings (Algebra)
Rings (Algebra) > Congresses
ISBN:147041032X, 9781470410322
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Summary: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.
Bibliography:Includes bibliographical references
Other editors: Alberto Facchini, André Leroy, Edmund Puczyłowski, Patrick Solé
ISBN:147041032X
9781470410322