On a New Class of Integral Domains with the Portable Property

Abstract

A (commutative integral) domain R is said to be a pseudo-almost divided domain if for all P ∈ Spec(R) and u ∈ PR P , there exists a positive integer n such that u n ∈ P. Such domains are related to several known kinds of domains, such as divided domains and straight domains. It is shown that “locally pseudo-almost divided” is a portable property of domains. Hence, if T is a domain with a maximal ideal Q and D is a subring of T∕Q, then the pullback \(R:= T \times _{T/Q}D\) is locally pseudo-almost divided if and only if both T and D are locally pseudo-almost divided. A similar pullback transfer result is given for the “straight domain” property (which is not known to be portable) by imposing additional restrictions on the data T, Q, D.