Arithmetical Properties of Commutative Rings and Monoids  book cover
1st Edition

Arithmetical Properties of Commutative Rings and Monoids

Edited By

Scott T. Chapman

ISBN 9780824723279
Published March 1, 2005 by CRC Press
416 Pages 4 B/W Illustrations

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Book Description

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.

Table of Contents

Non-Atomic Unique Factorization in Integral Domains
Daniel D. Anderson
Divisibility Properties in Graded Integral Domains
David F. Anderson
Extensions of Half-Factorial Domains: A Survey
Jim Coykendall
C-Monoids and Congruence Monoids in Krull Domains
Franz Halter-Koch
Monotone Chains of Factorizations in C-Monoids
Andreas Foroutan and Alfred Geroldinger
Transfer Principles in the Theory of Non-unique Factorizations
Alfred Geroldinger and Franz Halter-Koch
Cale Monoids, Cale Domains, and Cale Varieties
Scott T. Chapman and Ulrich Krause
Weakly Krull Inside Factorial Domains
Daniel D. Anderson, Muhammed Zafrullah, and Gyu Whan Chang
The m-Complement of a Multiplicative Set
David F. Anderson and Gyu Whan Chang
Some Remarks on Infinite Products
Jim Coykendall
Rings with Prime Nilradical
Ayman Badawi and Thomas G. Lucas
On the Ideal Generated by the Values of a Polynomial
Jean-Luc Chabert and Sabine Evrard
Using Factorizations to Prove a Partition Identity
David E. Dobbs and Timothy P. Kilbourn
On Inside Factorial Integral Domains
David E. Dobbs, Gabriel Picavet, and Martine Picavet-L'Hermitte
Polynomial Separation of Points in Algebras
Sophie Frisch
k-Factorized Elements in Telescopic Numerical Semigroups
Jose C. Rosales, Pedro A. Garcia-Sanchez, and Juan I. Garcia-Garcia
Prufer Conditions in Rings with Zero-Divisors
Sarah Glaz
Unmixedness and the Generalized Principal Ideal Theorem
Tracy Dawn Hamilton
A Note on Sets of Lengths of Powers of Elements of Finitely
Generated Monoids
Wolfgang Hassler
Evan Houston and Muhammad Zafrullah
On Local Half-Factorial Orders
Florian Kainrath
On Factorization in Krull Domains with Divisor Class
Group Z2k
Karl M. Kattchee
Integral Morphisms
Jack Maney
A Special Type of Invertible Ideal
Stephen McAdam and Richard G. Swan
Factorization into Radical Ideals
Bruce Olberding
Strongly Primary Ideals
Gyu Whan Chang, and Hoyoung Nam, and Jeanam Park

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