Arithmetical Properties of Commutative Rings and MonoidsScott T. Chapman 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 w |
Contents
| 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 |
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Common terms and phrases
Algebra Applied arithmetical assertion associated assume atomic base C-monoid called chapter characterization class group closure complete congruence consider construction contained Corollary D. F. Anderson Dedekind domain defined definition denote divides divisor elasticity elements equivalent example exists fact factorial integral domain factorization finite give given graded half-factorial Hence holds homogeneous homomorphism implies infinite product inside factorial integral integral domain integrally closed Introduction irreducible isomorphic Krull domain Krull monoid Lemma lengths locally Math maximal ideal minimal monoid multiplicative natural Nil(R Noetherian nonzero nonunit Note obtain particular polynomial positive primary prime ideal principal Proof Proposition prove Pure quotient field recall reduced representation resp respect result ring satisfies saturated semigroup strongly submonoid subset Suppose t-ideal Theorem theory torsion unique unit valuation domain zero