Vol. 46, No. 2, 1973

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(KE)-domains

Surjeet Singh

Vol. 46 (1973), No. 2, 561–574
Abstract

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 10 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 (p), the p-adic completion (p a prime number) of the ring Z of integers, is studied.

Mathematical Subject Classification 2000
Primary: 13G05
Milestones
Received: 30 June 1971
Revised: 30 November 1972
Published: 1 June 1973
Authors
Surjeet Singh