Algebras, Rings and Modules - Volume 1 (Hardcover, 2004 ed.)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Mathematics and Its Applications, 575
Release date:	October 2004
First published:	2004
Authors:	Michiel Hazewinkel • Nadiya Gubareni • V. V Kirichenko
Dimensions:	232 x 156 x 22mm (L x W x T)
Format:	Hardcover
Pages:	380
Edition:	2004 ed.
ISBN-13:	978-1-4020-2690-4
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	1-4020-2690-0
Barcode:	9781402026904

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