Factorization in Integral Domains, IV

Abstract

Let D be an integral domain such that every nonzero nonunit of D is a finite product of irreducible elements. In this article, we introduce and study several unifying concepts for the theory of nonunique factorization in D. They give a new way to measure, in some sense, how far an half-factorial domain (resp., bounded factorization domain, atomic domain) D is from being a UFD (resp., finite factorization domain, Cohen–Kaplansky domain) based on equivalence relations on the set of irreducible elements of D.

Key Words:

• Atomic domain
• Bounded factorization domain
• Cohen–Kaplansky domain
• Finite factorization domain
• Half-factorial domain
• Unique factorization

2000 Mathematics Subject Classification:

• Primary 13A05
• Secondary 13A15, 13F15, 13G05

Notes

Communicated by I. Swanson.