Introduction To Commutative Algebra (Google eBook)

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Westview Press, Feb 21, 1994 - Mathematics - 138 pages
4 Reviews
This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read
  

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Review: Introduction To Commutative Algebra

User Review  - Pietro - Goodreads

Read only the first couple of chapters. Proves strong results, with concise proofs. Not much intuition. Good exercises. Read full review

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Contents

Rings and Ideals
2
IDEALS QUOTIENT RINGS
3
PRIME IDEALS AND MAXIMAL IDEALS
4
NILRAOICAL AND JACOBSON RADICAL
6
OPERATIONS ON IDEALS
7
EXTENSION AND CONTRACTION
10
EXERCISES
11
Modules
18
THE GOINGUP THEOREM
62
INTEGRALLY CLOSED INTEGRAL DOMAINS THE GOINGDOWN THEOREM
63
VALUATION RINGS
66
EXERCISES
68
Chain Conditions
75
EXERCISES
79
Noetherian Rings
81
PRIMARY DECOMPOSITION IN NOETHERIAN RINGS
83

SUBMODULES AND QUOTIENT MODULES
19
OPERATIONS ON SUBMODULES
20
DIRECT SUM AND PRODUCT
21
FINITELY GENERATED MODULES
22
EXACT SEQUENCES
23
TENSOR PRODUCT OF MODULES
25
RESTRICTION AND EXTENSION OF SCALARS
28
EXACTNESS PROPERTIES OF THE TENSOR PRODUCT
29
ALGEBRAS
30
TENSOR PRODUCT OF ALGEBRAS
31
EXERCISES
32
Rings and Modules of Fractions
37
LOCAL PROPERTIES
41
EXTENDED AND CONTRACTED IDEALS IN RINGS OF FRACTIONS
42
EXERCISES
44
Primary Decomposition
51
EXERCISES
56
Integral Dependence and Valuations
60
EXERCISES
85
Artin Rings
90
EXERCISES
92
Discrete Valuation Rings and Dedekind Domains
94
DISCRETE VALUATION RINGS
95
DEDEKIND DOMAINS
96
TOPOLOGIES AND COMPLETIONS
102
FILTRATIONS
106
GRADED RINGS AND MODULES
107
THE ASSOCIATED GRADED RING
112
EXERCISES
114
11 Dimension Theory
117
DIMENSION THEORY OF NOETHERIAN LOCAL RINGS
120
REGULAR LOCAL RINGS
124
TRANSCENDENTAL DIMENSION
125
EXERCISES
126
Index
128
Copyright

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About the author (1994)

Sir Michael Atiyah was awarded the Fields Medal in 1966. He was elected a Fellow of the Royal Society in 1962 and received the Royal Medal of the Society in 1968 and its Copley Medal in 1988. He gave the Royal Society's Bakerian Lecture on Global geometry in 1975 and was President of the Royal
Society from 1990 to 1995.

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