Introduction to Abstract Algebra / / Kaiming Zhao, Libin Li.

• Superior document: Title is part of eBook package: De Gruyter DG Plus PP Package 2022 Part 2
• VerfasserIn: Li, Libin,; Zhao, Kaiming,
• Place / Publishing House: Les Ulis : : EDP Sciences, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: Current Natural Sciences
• Physical Description: 1 online resource (184 p.)

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.

Table of 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