Topics in Commutative Ring Theory - Hardcover

Watkins, John J.

Hardcover

ISBN 10: 0691127484 ISBN 13: 9780691127484

Publisher: Princeton University Press, 2007

Synopsis

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra.

Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics.

Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.

About this title

From the Back Cover

"A very elementary introduction to commutative ring theory, suitable for undergraduates with little background. It is written with great care, in a conversational and engaging style that I think will appeal to students. Essentially every detail is made explicit, and readers are admonished to beware typical pitfalls. The book is also peppered with very nice detours into the history of mathematics."--Karen Smith, University of Michigan

About the Author

John J. Watkins is professor of mathematics at Colorado College. He is the author of Across the Board: The Mathematics of Chessboard Problems (Princeton) and the coauthor of Graphs: An Introductory Approach.

Edition details

• Publisher: Princeton University Press
• Publication date: 2007
• ISBN 10: 0691127484
• ISBN 13: 9780691127484
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 232