http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs. avoids the formalism of category theory. aids independent study or seminarwork. and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
part 1 Fundamental Concepts / Jonathan S. Golan -- chapter Modules and Maps / Jonathan S. Golan -- chapter The Ring as a Module over Itself / Jonathan S. Golan -- part 1 Projectivity / Jonathan S. Golan -- chapter Coproducts of Copies of R (Free Modules) / Jonathan S. Golan -- chapter Direct Summands of Free Modules (Projective Modules) / Jonathan S. Golan -- chapter Submodules of Free Modules / Jonathan S. Golan -- chapter Factor Modules of Free Modules / Jonathan S. Golan -- part 2 Injectivity / Jonathan S. Golan -- chapter Enlarging Homomorphisms / Jonathan S. Golan -- chapter Embedding Modules in Injective Modules / Jonathan S. Golan -- chapter Injective Modules as a Class / Jonathan S. Golan -- chapter Structure of Injective Modules / Jonathan S. Golan -- part 3 Countability / Jonathan S. Golan -- chapter Finitely-Generated Modules / Jonathan S. Golan -- chapter Countably-Generated Modules / Jonathan S. Golan -- chapter Coproducts of Countably-Generated Modules / Jonathan S. Golan -- chapter Projective Modules / Jonathan S. Golan -- part 4 Part Four Rings and Modules of Quotients / Jonathan S. Golan -- chapter Torsion and Torsion free Modules / Jonathan S. Golan -- chapter The Module of Quotients / Jonathan S. Golan -- chapter Rings of Quotients / Jonathan S. Golan.