A ring R is called right mininjective if every isomorphism between sim
ple right ideals is given by left multiplication by an element of R. T
hese rings are shown to be Morita invariant. If R is commutative it is
shown that R is mininjective if and only if it has a squarefree socle
, and that every image of R is mininjective if and only if R has a dis
tributive lattice of ideals. If R is a semiperfect, right mininjective
ring in which eR has nonzero right socle for each primitive idempoten
t e, it is shown that R admits a Nakayama permutation of its basic ide
mpotents, and that its two socles are equal if every simple left ideal
is an annihilator. This extends well known results on pseudo- and qua
si-Frobenius rings. (C) 1997 Academic Press.