Algebra II: Textbook for Students of Mathematics - Hardcover

Gorodentsev, Alexey L.

Hardcover

ISBN 10: 3319508520 ISBN 13: 9783319508528

Publisher: Springer, 2017

Synopsis

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.

About this title

About the Author

A.L. Gorodentsev is professor at the Independent University of Moscow and  at the Faculty of Mathematics at the National Research University „Higher School of Economics“. 

He is working in the field of algebraic and symplectic geometry, homological algebra and representation theory connected with geometry of algebraic and symplectic varieties.

He is one of the first developers of the “Helix Theory” and semiorthogonal decomposition technique for studying the derived categories of coherent sheaves.

Review

“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) 

“This textbook contains fourteen chapters furnished with a lot of examples, counterexamples and numerous exercises, some of which are provided with commentary and hints, as well as problems for independent solution that were assigned as homework. ... This textbook is self-contained, well written and recommended to undergraduate, graduate and Ph. D. students and it might be very useful for advanced algebra lectures as well.” (Marek Golasiński, zbMATH, Vol. 1365.13001, 2017) 

Edition details

• Publisher: Springer
• Publication date: 2017
• ISBN 10: 3319508520
• ISBN 13: 9783319508528
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 385