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Undergraduate Algebra

A Unified Approach

  • Matej Brešar
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. The Language of Algebra

    1. Front Matter
      Pages 1-1
    2. Matej Brešar
      Pages 3-48
    3. Matej Brešar
      Pages 49-89
    4. Matej Brešar
      Pages 91-128
    5. Matej Brešar
      Pages 129-170
  3. Algebra in Action

    1. Front Matter
      Pages 171-171
    2. Matej Brešar
      Pages 173-222
    3. Matej Brešar
      Pages 223-250
    4. Matej Brešar
      Pages 251-310
  4. Back Matter
    Pages 311-316

About this book

Introduction

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.

Keywords

Algebra Abstract Algebra Groups Rings Fields Polynomials Integral domains Modules Sylow Theorems Galois Theory

Authors and affiliations

  • Matej Brešar
    • 1
  1. 1.Department of Mathematics, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-14053-3
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-14052-6
  • Online ISBN 978-3-030-14053-3
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site