Introduction to Abstract Algebra

This Third Edition of the acclaimed self-study text lets you learn abstract algebra at your own pace

The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields.The text's unique approach helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.

As in the previous editions, the Third Edition offers many special features to help readers learn and apply their developing knowledge of abstract algebra:

• Historical notes and biographies of mathematicians provide context and perspective
• Some 500 worked examples help readers understand key concepts and their applications
• Almost 1,500 computational and theoretical exercises ranging from basic to complex challenge readers to apply their knowledge to solve problems. Many answers are provided in the text
• Applications to real-world problems in such areas as coding theory and combinatorics help readers grasp the topic's relevancy
• Special topics such as symmetric polynomials, nilpotent groups, semidirect products of groups, and the Wedderburn-Artin theorem for rings are included for more advanced study

This Third Edition includes thoroughly revised chapters and much new material, including new sections covering free, semisimple, and projective modules; modules over principal ideal domains; as well as semidirect products and the Wedderburn-Artin theorem. Two new appendices have been added on Zorn's lemma and the proof of the recursion theorem.

Numerous worked examples, exercises, and real-world applications make this text perfect for upper-level undergraduate and graduate courses. Moreover, with this book's self-contained chapters, students can learn at their own pace, and instructors can adapt the text to meet a variety of course objectives.

W. KEITH NICHOLSON, PhD, is a Professor in the Department of Mathematics and Statistics at the University of Calgary in Alberta, Canada. Dr. Nicholson has published numerous textbooks and monographs throughout his career. He received his PhD in Pure Mathematics from the University of California at Santa Barbara, and his current research interests include clean rings, morphic rings, and module theory.