chapter  25
15 Pages

Factorization into Radical Ideals

ByBruce Olberding

In a paper of 1978 N. Vaughan and R. Yeagy prove that if a domain R has the property that every proper ideal is a product of radical ideals, then R is an almost Dedekind domain; that is, RM is a Dedekind domain for each maximal ideal M of R [19, Theorem 2.4]. Following Vaughan and Yeagy, we say that a ring R for which every proper ideal is a product of radical ideals (i.e. “semi-prime” ideals) is an SP -ring. Thus SP-domains are almost Dedekind.