Homological dimensions of modules
著者
書誌事項
Homological dimensions of modules
（Regional conference series in mathematics, no. 12）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1973
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注記
"Expository lectures from the CBMS regional conference held at the American University, Washington, District of Columbia, June 21-25, 1971."
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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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