Topics in Commutative Ring Theory (eBook)
by John J. Watkins (Author)

 17,009 Words
 232 Pages
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 setsuch as the integers, complex numbers, or polynomials with real coefficientswith two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian ringsone of the most important classes of commutative ringsand beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active readingroutine 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 settheoretic foundations of mathematics.
Written by an awardwinning 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.
 Released: February 9, 2009
 Categories: Education
 Language: English
 Publisher: Princeton University Press
 ISBN10: 1400828171
 ISBN13: 9781400828173