Arithmetical Properties of Commutative Rings and Monoids: 1st Edition (Paperback) book cover

Arithmetical Properties of Commutative Rings and Monoids

1st Edition

Edited by Scott T. Chapman

CRC Press

416 pages | 4 B/W Illus.

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pub: 2005-03-01
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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

About the Series

Lecture Notes in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Algebra / General