Rings whose proper (principal) right ideals are strongly compressible

Abstract

It is known that a ring R is semiprime right Goldie if and only if R-R is a strongly compressible module if and only if every right ideal of R is strongly compressible, and that a ring R is semiprime Goldie ring if and only if every right ideal of R is weakly injective if and only if every essential right ideal of R is weakly injective. In this paper, we characterize the rings whose proper (principal) right ideals are strongly compressible, and the rings whose proper (essential) right ideals are weakly injective.