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Titlebook: Associative Algebras; Richard S. Pierce Textbook 1982 Springer-Verlag New York Inc. 1982 Algebras.Assoziative Algebra.Category theory.Coho

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期刊全称Associative Algebras
影响因子2023Richard S. Pierce
视频video
学科分类Graduate Texts in Mathematics
图书封面Titlebook: Associative Algebras;  Richard S. Pierce Textbook 1982 Springer-Verlag New York Inc. 1982 Algebras.Assoziative Algebra.Category theory.Coho
影响因子For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine­ ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con­ tributes
Pindex Textbook 1982
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Modules, module theory constitutes a good foundation on which to erect the structure of rings and algebras. On the basis of this dictum, we begin our formal development with this chapter on modules. The emphasis is on semisimple modules, since these structures lead to semisimple algebras, the fundamental bu
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The Radical,are semisimple “up to a radical.” In fact, this is the case. All that is missing from a proof is the result that rad . is an ideal. We will establish this fact in Section 4.1. The rest of the chapter is concerned with properties and characterizations of the radical, a theorem about nilpotent algebra
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Representation of Quivers,P. Gabriel. He gave an explicit construction of the indecomposable modules for certain finite dimensional .-algebras. The most surprising part of Gabriel’s result is a link between the representation theory of algebras and the Dynkin diagrams that occur in the study of semisimple Lie algebras. This
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