SP-Domains are Almost Dedekind — A Streamlined Proof

Abstract

Let D be a domain. By [4], D has “property SP” if every ideal of D is a product of radical ideals. It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. In their article [4] Vaughan and Yeagy prove that a domain having property SP is an almost Dedekind domain. We give a very short and easy proof of this result.

Keywords

• sp-domain
• almost dedekind domain
• discrete valuation domain
• primary 13a15
• secondary 13f15