A right module A over a ring R is called finitely injective if every diagram of right R-modules
of the form where X is finitely generated and the row is exact, can be imbedded in a …

Almost Projective and Almost Injective Modules Page 1 ISSN 0001-4346, Mathematical
Notes, 2018, Vol. 103, No. 1, pp. 3–17. © Pleiades Publishing, Ltd., 2018. Original Russian …

Mares [9] has called a projective module semiperfect if every homomorphic image has a
projective cover and has shown that many of the properties of semiperfect rings can be …

In 1960, H. Bass [3] defined the notion of semi-perfect rings and, in 1963, E. Mares [ll]
generalized it to that of semi-perfect modules. Since that time various kinds of further …

ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …

Weakening the notion of R-projectivity, a right R-module M is called max-projective provided
that each homomorphism f: M→ R/I, where I is any maximal right ideal, factors through the …

1. Introduction. Modules M with the properties:(P1) every submodule N of M is essential in a
direct summand of M and (P2) every submodule N of M which is isomorphic to a direct …

Tachikawa showed that a left perfect ring R is an injective cogenerator in the category of all
right R-modules iff there holds:(right FPF) every finitely generated faithful right module …

This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …