Arithmetical Properties of Commutative Rings and Monoids

Front Cover
Scott T. Chapman
CRC Press, Mar 1, 2005 - Mathematics - 416 pages
The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the world to review recent major results. The first seven chapters demonstrate the diversity of approaches taken in studying nonunique factorizations and serve both as an introduction to factorization theory and as a survey of current trends and results. The remaining chapters reflect research motivated by arithmetical properties of commutative rings and monoids.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

NonAtomic Unique Factorization in Integral Domains
1
Divisibility Properties in Graded Integral Domains
22
Extensions of HalfFactorial Domains A Survey
46
CMonoids and Congruence Monoids in Krull Domains
71
Monotone Chains of Factorizations in CMonoids
99
Transfer Principles in the Theory of Nonunique Factorizations
114
Cale Monoids Cale Domains and Cale Varieties
142
Weakly Krull Inside Factorial Domains
172
Polynomial Separation of Points in Algebras
253
kFactorized Elements in Telescopic Numerical Semigroups
260
Prufer Conditions in Rings with ZeroDivisors
272
Unmixedness and the Generalized Principal Ideal Theorem
282
A Note on Sets of Lengths of Powers of Elements of Finitely Generated Monoids
293
UMVDomains
304
On Local HalfFactorial Orders
316
On Factorization in Krull Domains with Divisor Class Group Z2k
325

The mComplement of a Multiplicative Set
180
Some Remarks on Infinite Products
188
Rings with Prime Nilradical
198
On the Ideal Generated by the Values of a Polynomial
213
Using Factorizations to Prove a Partition Identity
226
On Inside Factorial Integral Domains
233
Integral Morphisms
337
A Special Type of Invertible Ideal
356
Factorization into Radical Ideals
363
Strongly Primary Ideals
378
Index
389
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information