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 ideal 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.

Provides a rigorous yet intuitive and accessible introduction to abstract algebra Treats conceptually similar themes from different areas of algebra in a unified manner Includes numerous examples and over 700 exercises

Autorentext

Matej Brear is a Professor at University of Ljubljana and University of Maribor. His research focus lies in noncommutative algebra and its applications. He is the author or co-author of over 160 research papers, the co-author of the monograph Functional Identities (Birkhauser, 2007), and the author of the graduate textbook Introduction to Noncommutative Algebra (Springer, 2014).

Inhalt
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.