Commutative Algebra

by Knight, J. T.

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Title Statements

Full title :Commutative Algebra.

Summary

Cover; Title; Copyright; Contents; 1. Preliminaries; 1. 1 INTRODUCTION; 1. 2 DEFINITIONS AND RECAPITULATIONS; 1.3 MODULES; 2. Flatness; 2.1 PROJECTIVE MODULES; 2.2 FLAT MODULES; 2.3 FAITHFULLY FLAT MODULES; 3. Fractions; 3.1 RINGS, MODULES AND ALGEBRAS OF FRACTIONS; 3.2 LOCALISATION; 3.3 PROJECTIVE MODULES AND LOCALISATION; 3.4 SUBMODULES OF FRACTION ALGEBRAS; 4. Supporting and associated prime ideals; 4.1 LENGTHS AND RANKS OF MODULES; 4.2 THE SUPPORT OF A MODULE; 4.3 PRIME IDEALS ASSOCIATED TO A MODULE; 5. Integers; 5.1 DEFINITION OF INTEGERS; 5.2 INTEGERS AND PRIME IDEALS.

6. Some geometrical resultsAPPLICATION TO ALGEBRAIC CLOSURES OF FIELDS; 7. Valuation rings; 7.1 ORDERED GROUPS; 7.2 VALUATION RINGS; 7.3 EXTENSION THEOREMS; 7.4 AN APPLICATION; EXAMPLES ON GENERAL VALUATIONS; 8. Prüfer and Dedekind rings; 9. General exercises; Appendix 1: A NOTE ON CATEGORIES, FUNCTORS AND NATURAL TRANSFORMATIONS; Appendix 2: THE CONSTRUCTIBLE TOPOLOGY; Bibliography; Index of notation; Index of terms.

This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry.

Edition Statements

Publication Date:1971.
Edition:Online-ausg

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:1971.

The Physical Object

Description:Online-Ressource (1 online resource (140 Seiten))

Edition Identifiers

ISBN:9781107093188, 110709318X, 9780511661822, 0511661827, 9780521081931, 0521081939
DOI:10.1017/CBO9780511661822
oclc:ocn852654172
LC Classification:QA251.3 .K55 1971
Dewey Decimal:512.24