Lectures on Rings and Modules

Fundamental Concepts of Algebra

* 1.1 Rings and related algebraic systems
* 1.2 Subrings, homomorphisms, ideals
* 1.3 Modules, direct products, and direct sums
* 1.4 Classical isomorphism theorems

Selected Topics on Commutative Rings

* 2.1 Prime ideals in commutative rings
* 2.2 Prime ideals in special commutative rings
* 2.3 The complete ring of quotients of a commutative ring
* 2.4 Rings of quotients of commutative semiprime rings
* 2.5 Prime ideal spaces

Classical Theory of Associative Rings

* 3.1 Primitive rings
* 3.2 Radicals
* 3.3 Completely reducible modules
* 3.4 Completely reducible rings
* 3.5 Artinian and Noetherian rings
* 3.6 On lifting idempotents
* 3.7 Local and semiperfect rings

Injectivity and Related Concepts

* 4.1 Projective modules
* 4.2 Injective modules
* 4.3 The complete ring of quotients
* 4.4 Rings of endomorphisms of injective modules
* 4.5 Regular rings of quotients
* 4.6 Classical rings of quotients
* 4.7 The Faith-Utumi theorem

Introduction to Homological Algebra

* 5.1 Tensor products of modules
* 5.2 Hom and $\otimes$ as functors
* 5.3 Exact sequences
* 5.4 Flat modules
* 5.5 Torsion and extension products

* Appendixes
* Comments
* Bibliography
* Index