Commutative Semigroup Rings

Robert Gilmer

Commutative Semigroup Rings
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Robert Gilmer

390 pages | © 1984
Paper $40.00 ISBN: 9780226293929 Published March 1984
Commutative Semigroup Rings was the first exposition of the basic properties of semigroup rings.  Gilmer concentrates on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.
Contents
PREFACE
I.    COMMUTATIVE  SEMIGROUPS
1. Basic Notions
2.  Cyclic Semigroups and Numerical Monoids
3.  Ordered  Semigroups
4.  Congruences
5.  Noetherian  Semigroups
6.  Factorization in Commutative Monoids
II.   SEMIGROUP RINGS AND THEIR DISTINGUISHED ELEMENTS
7.  Semigroup Rings
8.  Zero  Divisors
9.  Nilpotent Elements
10.  Idempotents
11.  Units
III. RING-THEORETIC PROPERTIES OF MONOID DOMAINS
12.  Integral Dependence for Monoid Domains
13. Monoid Domains as Priifer Domains
14. Monoid Domains as Factorial Domains
15. Monoid Domains as Krull Domains
16.  The Divisor Class Group of a Krull Monoid Domain
IV. RING-THEORETIC PROPERTIES OF MONOID RINGS
17. Monoid Rings as von Neumann Regular Rings
18.  Monoid  Rings  as  PrUfer  Rings
19.  Monoid Rings as Arithmetical Rings the Case Where  S   is not Torsion-Free
20.  Chain Conditions in Monoid Rings
V.   DIMENSION THEORY AND THE ISOMORPHISM PROBLEMS
21. Dimension Theory of Monoid Rings
22.  R-Automorphisms  of  R[S]
23.  Coefficient Rings in Isomorphic Monoid Rings. I
24.  Coefficient Rings in Isomorphic Monoid Rings. 11
25. Monoids In Isomorphic Monoid Rings - a Survey
SELECTED BIBLIOGRAPHY
TOPIC   INDEX
INDEX OF MAIN NOTATION
INDEX OF SOME MAIN RESULTS
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