ロシア式代数学テキスト2<br>Algebra II〈1st ed. 2017〉 : Textbook for Students of Mathematics

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ロシア式代数学テキスト2
Algebra II〈1st ed. 2017〉 : Textbook for Students of Mathematics

  • 著者名:Gorodentsev, Alexey L.
  • 価格 ¥6,139 (本体¥5,685)
  • Springer(2017/02/12発売)
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Description

This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings,&nbsp;modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The&nbsp;course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra,&nbsp;representation theory,&nbsp;category theory, commutative algebra, Galois theory, and algebraic&nbsp;geometry – topics that are often overlooked in standard undergraduate courses.This textbook is based on courses the author has conducted at the Independent University of Moscow and at&nbsp;the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for&nbsp;independent study.

Table of Contents

§1Tensor Products.- §2 Tensor Algebras.- §3 Symmetric Functions.- §4 Calculus of Arrays, Tableaux, and Diagrams.- §5 Basic Notions of Representation Theory.- §6 Representations of Finite Groups in Greater Detail.- §7 Representations of Symmetric Groups.- §8 sl_2-Modules.- §9 Categories and Functors.- §10 Extensions of Commutative Rings.- §11 Affine Algebraic Geometry.- §12 Algebraic Manifolds.- §13 Algebraic Field Extensions.- §14 Examples of Galois Groups.- References.- Hints to Some Exercises.- Index.