A commutative ring R is
said to have the (K)-property if for each of its proper ideals A, there exists an ideal
A′, such that AAr is a nonzero principal ideal of R. A domain D with unity 1≠0 is
said to be a (KE)-domain, if each of its ideals A, considered as a ring, has the
(K)-property. The concept of a (KE)-domain had been studied earlier by the
author and R. Kumar. In this paper injective modules and flat modules are
studied and characterizations of (KE). domains in terms of these modules
are established. Finally the problem of embedding of a (KE)-domain in
Ẑ(p), the p-adic completion (p a prime number) of the ring Z of integers, is
studied.
