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Undergraduate algebra : a unified approach

Author: Matej Brešar
Publisher: Cham : Springer, [2019]
Series: Springer undergraduate mathematics series.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1083457273
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Matej Brešar
ISBN: 9783030140533 3030140539
OCLC Number: 1103468530
Notes: Includes index.
Description: 1 online resource
Contents: Preface --
1 Glossary of Basic Algebraic Structures --
2 Examples of Groups and Rings --
3 Homomorphisms --
4 Quotient Structures --
5 Commutative Rings --
6 Finite Groups --
7 Field Extensions --
Frequently Used Symbols --
Index.
Series Title: Springer undergraduate mathematics series.
Responsibility: Matej Brešar.

Abstract:

This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal integral domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.

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