ABSTRACT
Like its popular predecessors, this text develops ring theory first by drawing on students' familiarity with integers and polynomials. This unique approach motivates students in studying abstract algebra and helps them understand the power of abstraction. This edition makes it easier to teach unique factorization as an optional topic and reorganizes the core material on rings, integral domains, and fields. Along with new exercises on Galois theory, it also includes a more detailed treatment of permutations as well as new chapters on Sylow theorems.
TABLE OF CONTENTS
part 1|2 pages
Part I: Numbers, Polynomials, and Factoring
part |2 pages
Part II: Rings, Domains, and Fields
part 3|2 pages
Part III: Ring Homomorphisms and Ideals
part 4|2 pages
Part IV: Groups
part 5|2 pages
Part V: Group Homomorphisms
part 6|2 pages
Part VI: Topics from Group Theory
part 7|2 pages
Part VII: Unique Factorization
part 8|2 pages
Part VIII: Constructibility Problems
part 9|2 pages
Part IX: Vector Spaces and Field Extensions
part 10|2 pages
Part X: Galois Theory