MARC Record from harvard_bibliographic_metadata

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050 4 $aQA247$b.H29 2004
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082 04 $a512.42$222
100 1 $aHazewinkel, Michiel.
245 00 $aAlgebras, rings and modules /$bby Michiel Hazewinkel, Nadiya Gubareni, and V. V. Kirichenko.
260 $aDordrecht :$bKluwer,$cc2004-2007.
300 $a2 v. :$bill. ;$c24 cm.
490 1 $aMathematics and its applications ;$vv. 575, 586
504 $aIncludes bibliographical references and indexes.
505 0 $aPreliminaries -- Decompositions of rings -- Artinian and Noetherian rings -- Categories and functors -- Projectives, injectives and flats -- Homological dimensions -- Integral domains -- Dedekind domains -- Goldie rings -- Semiperfect rings -- Quivers of rings -- Serial rings and modules -- Serial rings and their properties -- Semiperfect semidistributive rings.
520 $aAccosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.
650 6 $aAnneaux (Algèbre)
650 6 $aModules (Algèbre)
650 0 $aRings (Algebra)
650 0 $aModules (Algebra)
650 0 $aAlgebra.
650 0 $aMathematics.
700 1 $aGubareni, Nadezhda Mikhaĭlovna.
700 1 $aKirichenko, Vladimir V.
830 0 $aMathematics and its applications (Kluwer Academic Publishers) ;$vv. 575, 586.
988 $a20080303
906 $0OCLC