Rings and categories of modules / Frank W. Anderson, Kent R. FullerType de document : MonographieCollection : Graduate texts in mathematics, 13Langue : anglais.Pays : Etats Unis.Mention d'édition: 2nd editionÉditeur : New York : Springer, 1992Description : 1 vol. (VIII-376 p.) ; 24 cmISBN : 0387978453.ISSN : 0072-5285.Bibliographie : Bibliogr. p. 363-368. Index.Sujet MSC : 16-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
16D90, Modules, bimodules and ideals in associative algebras, Module categories in associative algebras; module theory in a category-theoretic context; Morita equivalence and duality
16P20, Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras, Artinian rings and modulesEn-ligne : Springerlink | Zentralblatt | MathSciNet
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From the preface: Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, decomposition theory of injective and projective modules, and semiperfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have helped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory.
Bibliogr. p. 363-368. Index