UID:
almahu_9949697318102882
Format:
1 online resource (317 p.)
ISBN:
1-281-76656-9
,
9786611766566
,
0-08-087356-1
Series Statement:
Pure and applied mathematics; a series of monographs and textbooks ; v. 43
Content:
Multiplicative theory of ideals
Note:
Description based upon print version of record.
,
Front Cover; MULTIPLICATIVE THEORY OF IDEALS; Copyright Page; Contents; Preface; Prerequisites; Chapter I. Modules; 1 Rings and Modules; 2 Chain Conditions; 3 Direct Sums; 4 Tensor Products; 5 Flat Modules; Exercises; Chapter II. Primary Decompositions and Noetherian Rings; 1 Operations on Ideals and Submodules; 2 Primary Submodules; 3 Noetherian Rings; 4 Uniqueness Results for Primary Decompositions; Exercises; Chapter III. Rings and Modules of Quotients; 1 Definition; 2 Extension and Contraction of Ideals; 3 Properties of Rings of Quotients; Exercises; Chapter IV. Integral Dependence
,
1 Definition of Integral Dependence2 Integral Dependence and Prime Ideals; 3 Integral Dependence and Flat Modules; 4 Almost Integral Dependence; Exercises; Chapter V. Valuation Rings; 1 The Definition of a Valuation Ring; 2 Ideal Theory in Valuation Rings; 3 Valuations; 4 Prolongation of Valuations; Exercises; Chapter Vl. Prüfer and Dedekind Domains; 1 Fractional Ideals; 2 Prüfer Domains; 3 Overrings of Prüfer Domains; 4 Dedekind Domains; 5 Extension of Dedekind Domains; Exercises; Chapter VII. Dimension of Commutative Rings; 1 The Krull Dimension; 2 The Krull Dimension of a Polynomial Ring
,
3 Valuative DimensionExercises; Chapter VIII. Krull Domains; 1 Krull Domains; 2 Essential Valuations; 3 The Divisor Class Group; 4 Factorial Rings; Exercises; Chapter IX. Generalizations of Dedekind Domains; 1 Almost Dedekind Domains; 2 ZPI-Rings; 3 Multiplication Rings; 4 Almost Multiplication Rings; Exercises; Chapter X. Prüfer Rings; 1 Valuation Pairs; 2 Counterexamples; 3 Large Quotient Rings; 4 Prüfer Rings; Exercises; Appendix: Decomposition of ideals in Noncommutative Rings; Exercises; Bibliography; Subject Index; Pure and Applied Mathematics: A Series of Monographs and Textbooks
,
English
Additional Edition:
ISBN 0-12-436850-6
Language:
English
