272 Pages
by
CRC Press
288 Pages
by
CRC Press
272 Pages
by
CRC Press
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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... Read more
Part I: Fundamental Concepts Modules and Maps 1. The Ring as a Module over Itself Part II: Projectivity 2. Coproducts of Copies of R (Free Modules) 3. Direct Summands of Free Modules (Projective Modules) 4. Submodules of Free Modules 5. Factor Modules of Free Modules Part III: Injectivity 6. Enlarging Homomorphisms 7. Embedding Modules in Injective Modules 8. Injective Modules as a Class 9. Structure of Injective Modules Part IV: Countability 10. Finitely-Generated Modules 11. Countably-Generated Modules 12. Coproducts of Countably-Generated Modules 13. Projective Modules Part V: Rings and Modules of Quotients 14. Torsion and Torsion free Modules 15. The Module of Quotients 16. Rings of Quotients
Biography
Golan,
