Algebra II Textbook for Students of Mathematics [Paperback]

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,?modules, algebras, groups, and categories  and explains the main principles of and methods for working with them.

The?course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra,?representation theory,?category theory, commutative algebra, Galois theory, and algebraic?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?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?independent study.

?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.

This is the second of a two-volume set of books offering a Russian-style intensive introduction to abstract algebra. & Each chapter contains both exercises that are imbedded in the text, and problems that are collected at the end of each chapter. & In summary, this book, like its predecessor, seems to have been written for mathematicians & . (Mark Hunacek, MAA Reviews, March, 2017)?