Weakly Krull domains and the composite numerical semigroup ring D + E[Γ^∗]

Jung Wook Lim

Vol. 257 (2012), No. 1, 227–242

DOI: 10.2140/pjm.2012.257.227

Abstract

Let D ⊆ E be an extension of integral domains, Γ a numerical semigroup with Γ ⊊ ℕ₀, Γ^∗ = Γ ∖{0} and R = D + E[Γ^∗]. In this paper, we completely characterize when R is a weakly Krull domain, an AWFD or a GWFD. We also prove that R is never a WFD.

Keywords

numerical semigroup, D + E[Γ^∗], weakly Krull domain

Mathematical Subject Classification 2010

Primary: 13A15, 13G05

Secondary: 13A02, 13B25, 13F05

Milestones

Received: 17 September 2011

Revised: 10 April 2012

Accepted: 16 April 2012

Published: 19 June 2012