Introduction to Abstract Algebra / Libin Li and Kaiming Zhao.

Format:

Book

Author/Creator:

Li, Libin, author.

Zhao, Kaiming, author.

Series:

Current Natural Sciences.

Current Natural Sciences Series

Language:

English

Subjects (All):

Algebra, Abstract.

Physical Description:

1 online resource (184 pages).

Edition:

First edition.

Place of Publication:

Les Ulis, France : EDP Sciences, [2022]

Summary:

Abstract algebra is an essential tool in algebra, number theory, geometry, topology, and, to a lesser extent, analysis. It is therefore a core requirement for all mathematics majors. Outside of mathematics, abstract algebra also has many applications in cryptography, coding theory, quantum chemistry, and physics.This book is intended as a textbook for a one-term senior undergraduate or gradate course in abstract algebra to prepare students for further readings on relevant subjects such as Group Theory and Galois Theory. Abstract algebra being the field of mathematics that studies algebraic structures such as groups, rings, fields, and modules, we will primarily study groups, rings, and fields in this book. The authors invite readers to experience the beauty of mathematics by studying Abstract algebra which offers not only opportunities to work on complex concepts and to develop one’s abstract reasoning abilities, but also a preliminary understanding of what it is like to do research in mathematics.Libin LI is professor at School of Mathematics, Yangzhou University in China. His research interests include Representation theory in Hopf algebras and Tensor category, Decoding theory and Ring theory, Weyl algebras and isomorphism problems, etc.

Contents:

Frontmatter

Preface

Contents

Notations

Chapter 1. Groups and Generating Sets

Chapter 2. Permutation Groups and Alternating Groups

Chapter 3. Finitely Generated Abelian Groups and Quotient Groups

Chapter 4. Rings, Quotient Rings and Ideal Theory

Chapter 5. Unique Factorization Domains

Chapter 6. Extension Fields

Appendix A. Equivalence Relations and Quotient Set

Appendix B. Zorn's Lemma

Appendix C. Quotient field

Reference

Index

Notes:

Includes bibliographical references and index.

Description based on: online resource; title from PDF information screen (De Gruyter, viewed November 25, 2022).

Description based on print version record.

ISBN:

9782759829163

2759829162

OCLC:

1343104564