Commutative Semigroup Rings

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University of Chicago Press, Mar 15, 1984 - Mathematics - 380 pages
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.
 

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Contents

COMMUTATIVE SEMIGROUPS
1
Basic Notions
2
Cyclic Semigroups and Numerical Monoids
9
Ordered Semigroups
22
Congruences
28
Noetherian Semigroups
39
Factorization in Commutative Monoids
52
SEMIGROUP RINGS AND THEIR DISTINGUISHED ELEMENTS
63
The Divisor Class Group of a Krull Monoid Domain
208
RINGTHEORETIC PROPERTIES OF MONOID RINGS
225
Monoid Rings as von Neumann Regular Rings
226
Monoid Rings as Priifer Rings
240
Monoid Rings as Arithmetical Rings the Case Where S is not TorsionFree
253
Chain Conditions in Monoid Rings
271
DIMENSION THEORY AND THE ISOMORPHISM PROBLEMS
287
Dimension Theory of Monoid Rings
288

Semigroup Rings
64
Zero Divisors
82
Nilpotent Elements
97
Idempotents
113
Units
129
RINGTHEORETIC PROPERTIES OF MONOID DOMAINS
145
Integral Dependence for Monoid Rings
147
Monoid Domains as Prufer Domains
162
Monoid Domains as Factorial Domains
171
Monoid Domains as Krull Domains
190
Rautomorphisms of RS
303
Coefficient Rings in Isomorphic Monoid Rings I
317
Coefficient Rings in Isomorphic Monoid Rings II
337
Monoids in Isomorphic Monoid Rings a Survey
351
SELECTED BIBLIOGRAPHY
355
TOPIC INDEX
363
INDEX OF MAIN NOTATION
371
INDEX OF SOME MAIN RESULTS
375
Copyright

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