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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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Noncommutative Rings and Their Applications (Conference) Sole, Patrick Leroy, Andre (Andre Gerard) Facchini, Alberto Puczylowski, Edmund Dougherty, Steven |
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| Notes | Includes bibliographical references Other editors: Alberto Facchini, André Leroy, Edmund Puczyłowski, Patrick Solé |
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| SubjectTerms | 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 |
| Title | Noncommutative rings and their applications : International Conference on Noncommutative Rings and Their Applications, July 1-4, 2013, Université d'Artois, Lens, France |
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