In this paper, by a left QF-3 ring we shall always understand a ring with a (unique) minimal
faithful left module, and by a QF-3 ring we mean a ring which is both left and right QF-3 …

In a recent paper (which is to appear in J. Algebra Appl.) we proved that every element of a
right self-injective ring R is a sum of two units if and only if R has no factor ring isomorphic to …

A ring R is called right FP-injective if every R-homomor-phism from a finitely generated
submodule of a free right R-module F into R extends to F. In this paper a ring R will be called …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

A ring R is called a right PCI-ring if and only if for any cyclic right R-module C either C≅ R or
C is injective. Faith has shown that right PCI-rings are either semiprime Artinian or simple …

Abstract A right R-module C is proper cyclic in case R→ C→ 0 is exact but 0→ R→ C→ 0 is
not. A ring R is a ring PCI ring if every proper cyclic right R-module is injective (PC⇒ I ring”) …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

Necessary and sufficient conditions on a ring R are found under which all surjective
endomorphisms of finitely generated right R-modules are automorphisms. Namely, this …