CBMS Regional Conference Series in Mathematics 1973; 89 pp; softcover Number: 12 Reprint/Revision History: third printing 1995 ISBN10: 0821816624 ISBN13: 9780821816622 List Price: US$23 Member Price: US$18.40 All Individuals: US$18.40 Order Code: CBMS/12
 These notes were prepared for a series of ten lectures given at Regional Conference of the Conference Board of the Mathematical Sciences in June 1971. The bulk of the lectures were on projective dimensions of "very large" modules. Although the material in these notes is not new, there are several places where existing work has been simplified. For example, a commutative local nondomain of global dimension 3 is described without reference to analysis, and the dimension of a quotient field of a polynomial ring rather than a regular local ring is calculated. A derivation of Tor, one step at a time without the usual derived functor machinery, is also included. Readership Table of Contents Part I. Introductory ring and category theory  General definitions, notations, examples
 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
