ABSTRACT
New classes of locally divided rings R are introduced in two ways: by requiring all CPI‐extensions of R to be special types of rings of fractions and by requiring all localizations of R to be pseudo‐valuation rings. For rings R whose zero‐divisors are nilpotent and whose minimal prime ideal is divided, the first method characterizes the locally divided R in which each nonminimal prime ideal is contained in a unique maximal ideal. The second method, concerning LPVRs, focuses on idealization, for which a typical result is the following. If E is a module over an integral domain R, then R (+) E is an LPVR if and only if R is an LPVD and EM is a divisible RM ‐module for each maximal ideal M of R.
