Modules and the Structure of Rings

This textbook is designed for students with at least one solid semester of abstract algebra, some linear algebra background, and no previous knowledge of module theory.

Modules and the Structure of Rings details the use of modules over a ring as a means of considering the structure of the ring itself—explaining the mathematics and inductive reasoning used in working on ring theory challenges and emphasizing modules instead of rings.

Stressing the inductive aspect of mathematical research underlying the formal deductive style of the literature, this volume offers vital background on current methods for solving hard classification problems of algebraic structures.

Written in an informal but completely rigorous style, Modules and the Structure of Rings clarifies sophisticated proofs ... avoids the formalism of category theory ... aids independent study or seminar work ... and supplies end-of-chapter problems.

This book serves as an excellent primary text for upper-level undergraduate and graduate students in one-semester courses on ring or module theory—laying a foundation for more advanced study of homological algebra or module theory.