Mininjective rings

A ring R is called right mininjective if every isomorphism between simple right ideals is given by left multiplication by an element of R. These 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 distributive lattice of ideals. If R is a semiperfect, right mininjective ring in which eR has nonzero right socle for each primitive idempotent e, it is shown that R admits a Nakayama permutation of its basic idempotents, and that its two socles are equal if every simple left ideal is an annihilator. This extends well known results on pseudo- and quasi-Frobenius rings. (C) 1997 Academic Press.