Abstract
Introduction Part I. Introductory ring and category theory: General definitions, notations, example Basic properties of projectives, injectives, flat modules, Hom and $\otimes$ Basic commutative algebra Part II. Homological dimensions: Definitions of various dimensions, Ext, and Tor An alternative derivation of Tor and Ext Elementary applications Commutative algebra revisited Set theoretic propositions Not so elementary applications and counting theorems More counting Appendix. Introductory set theory Notation, definitions, basic axioms Cardinals, ordinals, and the axiom of choice Bibliographical notes.
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