Arithmetical properties of commutative rings and monoids


Arithmetical properties of commutative rings and monoids

[edited by] Scott T. Chapman

(Lecture notes in pure and applied mathematics, v. 241)

CRC Press/Taylor & Francis, 2005

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"This volume contains the proceedings of two related meetings which took place in October 2003."--Pref

Includes bibliographies and index



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.


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 UMV-Domains 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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