Arithmetical Properties of Commutative Rings and Monoids

Scott T. Chapman

• Publisher: CRC Press
• Year: 2005
• Topic: Mathematics
• eBook ISBN:
  9781040205334
• Subtopic: Algebra
• Index: Mathematics

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

Table of contents

• Cover Page
• Halftitle Page
• PURE AND APPLIED MATHEMATICS
• LECTURE NOTES IN PURE AND APPLIED MATHEMATICS
• Title Page
• Copyright Page
• Preface
• Contents
• Contributors
• 1 Non-Atomic Unique Factorization in Integral Domains
• 2 Divisibility Properties in Graded Integral Domains
• 3 Extensions of Half-Factorial Domains: A Survey
• 4 C-Monoids and Congruence Monoids in Krull Domains
• 5 Monotone Chains of Factorizations in C-Monoids
• 6 Transfer Principles in the Theory of Non-unique Factorizations
• 7 Cale Monoids, Cale Domains, and Cale Varieties
• 8 Weakly Krull Inside Factorial Domains
• 9 The m-Complement of a Multiplicative Set
• 10 Some Remarks on Infinite Products
• 11 Rings with Prime Nilradical
• 12 On the Ideal Generated by the Values of a Polynomial
• 13 Using Factorizations to Prove a Partition Identity
• 14 On Inside Factorial Integral Domains
• 15 Polynomial Separation of Points in Algebras
• 16 k-Factorized Elements in Telescopic Numerical Semigroups
• 17 Prüfer Conditions in Rings with Zero-Divisors
• 18 Unmixedness and the Generalized Principal Ideal Theorem
• 19 A Note on Sets of Lengths of Powers of Elements of Finitely Generated Monoids
• 20 UMV-Domains
• 21 On Local Half-Factorial Orders
• 22 On Factorization in Krull Domains with Divisor Class Group Z2k
• 23 Integral Morphisms
• 24 A Special Type of Invertible Ideal
• 25 Factorization into Radical Ideals
• 26 Strongly Primary Ideals
• Index