A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Characterization of Rings Using Quasiprojective Modules. II Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 28, Number 2, May 1971 CHARACTERIZATION …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

The notion of generalized projective covers Is Introduced to give a natural generalization of
a theorem of Bass on perfect rings. Moreover, In terms of this notion, some characterizations …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

The purpose of this paper is to initiate the study of improjective modules. A module X is im-
projective if given any epimorphism/: B-> A and any homomorphism/: X-> A, there exists a …

Let R be a ring and M a fixed R-module. An R-module Q is called M-injective if, given a
monomorphism C $ of an R-module N into M, every homomorphism: N-+ Q can be extended …

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 …

Recently,]~. DE ROBERT has considered the dual concepts of relative projectivity and
relative injectivity that extend the notions of quasi-projective and quasi-injective modules …