Modules and the Structure of Rings: A Primer

ISBN-13: 9780824785550 / Angielski / Twarda / 1991 / 272 str.

Jonathan S. Golan;Golan

Opis

This book offers vital background information on methods for solving hard classification problems of algebraic structures. It explains how algebraists deal with the problem of the structure of modules over rings and how they make use of these structures to classify rings.

Spis treści

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

O autorze

Golan\,