Algebras, rings and modules: Vol. 1

Book Cover
Kluwer Academic Publishers,
Pub. Date:
Accosiative 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.
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full_title algebras rings and modules vol 1
author hazewinkel michiel
grouping_category book
lastUpdate 2018-01-31 01:40:13AM

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auth_author2 Gubareni, Nadezhda Mikhaĭlovna., Kirichenko, Vladimir V.
author Hazewinkel, Michiel.
author2-role Gubareni, Nadezhda Mikhaĭlovna., Kirichenko, Vladimir V., SpringerLink (Online service)
author_display Hazewinkel, Michiel
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publishDate 2004
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series Mathematics and its applications
series_with_volume Mathematics and its applications|v. 575.
subject_facet Electronic books, Modules (Algebra), Rings (Algebra)
title_display Algebras, rings and modules. Vol. 1
title_full Algebras, rings and modules. Vol. 1 [electronic resource] / by Michiel Hazewinkel, Nadiya Gubareni and V.V. Kirichenko
title_short Algebras, rings and modules
title_sub Vol. 1
topic_facet Modules (Algebra), Rings (Algebra)