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Basic abstract algebra : for graduate students and advanced undergraduates

Author: Robert B Ash
Publisher: Mineola, N.Y. : Dover Publications, 2007. ©2007
Series: Dover books on mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic
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Genre/Form: Textbooks
Electronic books
Additional Physical Format: Print version:
Ash, Robert B.
Basic abstract algebra.
Mineola, N.Y. : Dover Publications, ©2007
(DLC) 2006048618
(OCoLC)70778380
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Robert B Ash
ISBN: 9780486318110 0486318117
OCLC Number: 853622313
Description: 1 online resource (xi, 407 pages).
Contents: Group fundamentals --
Ring fundamentals --
Field fundamentals --
Module fundamentals --
Some basic techniques of group theory --
Galois theory --
Introducing algebraic number theory --
Introducing algebraic geometry --
Introducing noncommutative algebra --
Introducing homological algebra.
Series Title: Dover books on mathematics.
Responsibility: Robert B. Ash, Department of Mathematics, University of Illinois.
More information:

Abstract:

Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

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