On a semiprimary ring

Let R be a ring with 1 having radical (Jacobson) N. R is called semiprimary [2, p. 56] if and only if R/N satisfies the minimum condition for right ideals. If M is a right R-module, a submodule A of M is called small [5] if A +B M for any submodule B of M implies B = M. A submodule A of M is called large [3] if A (B -0 for any submodule B of M implies B = 0. A right ideal in R is called small or large if I is small or large as a submodule of the right regular Rmodule RR. A projective cover [1 ] of M is an epimorphism of a projective module onto M such that its kernel is small. The main results of this paper are the following theorems: