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Farb B., Dennis R.K. — Noncommutative Algebra (Graduate Texts in Mathematics)
Farb B.,  Dennis R.K. — Noncommutative Algebra (Graduate Texts in Mathematics)

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Название: Noncommutative Algebra (Graduate Texts in Mathematics)

Автор: Farb B., Dennis R.K.

Аннотация:

This book is an introduction to the theory of noncommutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semisimple modules and rings, including the Wedderburn structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of finite groups is combined with the Wedderburn Structure Theorem to prove Burnside’s Theorem; the global dimension of a ring is studied using Kaplansky’s elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Указатель в процессе заполнения

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 227

Добавлена в каталог: 23.10.2011

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