On principally small-injective rings

A ring R is called right (left) principally small (PS)-injective if every R-homomorphism from a principal right (left) ideal contained in the Jacobson radical of R into R is given by left (right) multiplication by an element of R. In this work, we investigate various properties of the principal right (left) ideals of a right (left) PS-injective ring R. We also record some results on rings whose singular simple right (left) modules are PS-injective. Further, we obtain a characterization of PS-injective group rings.