Special Principal Ideal Rings and Absolute Subretracts

Abstract

AbstractA ringRis said to be an absolute subretract if for any ringSin the variety generated byRand for any ring monomorphismffromRintoS, there exists a ring morphismgfromStoRsuch that gf is the identity mapping. This concept, introduced by Gardner and Stewart, is a ring theoretic version of an injective notion in certain varieties investigated by Davey and Kovacs.Also recall that a special principal ideal ring is a local principal ring with nonzero nilpotent maximal ideal. In this paper (finite) special principal ideal rings that are absolute subretracts are studied.