On the integral closure of a half-factorial domain

✍ Scribed by Jim Coykendall

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 115 KB
• Volume: 180
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00303-1

✦ Synopsis

A half-factorial domain (HFD), R, is an atomic integral domain where given any two products of irreducible elements of R:

As a natural generalization of unique factorization domains (UFD), one wishes to investigate which "good" properties of UFDs that HFDs possess. In particular, it has been conjectured that the integral closure of a half-factorial domain is again a HFD (see Non-Noetherian Commutative Ring Theory, Mathematics and its applications, Vol. 520,