Bézout SP-Domains

Abstract

SP-domains were first introduced by Vaughan and Yeagy (1978) as generalizations of Dedekind domains. In particular, they showed that an SP-domain is an almost Dedekind domain. Later, Olberding (2005) gave a complete characterization of SP-domains within the class of almost Dedekind domains. This article characterizes Bézout SP-domains using the order structure of the group of divisibility of an integral domain. We use this information to construct a Bézout SP-domain with zero Jacobson radical.

Key Words:

• Bézout domain
• Lattice-ordered group of divisibility
• Specker group

Mathematics Subject Classification:

• Primary 13F05
• Secondary 06F20

Notes

Communicated by K. M. Rangaswamy.