Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields

This book is a comprehensive textbook on abstract algebra, covering set theory, group theory, ring and ideal theory, field theory, and Dedekind rings. It provides a fresh perspective on the subjects, with distinctive treatments of factorization theory and Galois theory. It assumes no prior knowledge of abstract algebra and is illustrated by many examples. Each chapter concludes with exercises to reinforce students' knowledge.

Format: Hardback
Length: 438 pages
Publication date: 26 June 2022
Publisher: World Scientific Publishing Co Pte Ltd

This comprehensive textbook serves as a foundational resource for a semester-long or year-long introductory course in abstract algebra, catering to upper undergraduate and beginning graduate students. It delves into various branches of algebra, including set theory, group theory, ring and ideal theory, and field theory, culminating in a detailed exploration of Dedekind rings, encompassing rings of algebraic integers. In addition to covering standard topics, the book offers unique insights into factorization theory in integral domains and Galois theory, presenting a fresh perspective on these subjects. While it assumes no prior knowledge of abstract algebra, it provides a well-motivated, clear, and rigorous treatment, accompanied by numerous examples to illustrate key concepts. Written with an emphasis on number theory, the text incorporates numerous applications to number theory, such as proofs of Fermat's theorem on sums of two squares and the Law of Quadratic Reciprocity. It serves as an excellent foundation for further study in algebra and number theory, with each chapter concluding with a range of exercises to reinforce students' understanding of the material. These exercises span from straightforward to challenging, fostering a deeper grasp of the subject matter.

ISBN-13: 9789811246661