Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image
of M. It is shown that if R is a right perfect ring, then every projective slightly compressible …

Let R be a commutative Noetherian ring and I, J two ideals of R. Let M be a finitely
generated R-module; it is shown that (1) if dimR/(I+ J)= 0, then Hi I, J (M)/JHi I, J (M) is I …

Let R be a commutative Noetherian ring and M a finitely generated R-module. Under various
hypotheses, it is proved that the center of End R (M) coincides with the endomorphism ring …

We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a
direct sum of countably generated modules [2, Theorem l]. If any direct summand A of a …

A right R-module M is called quasi-principally injective if every homomorphism from an M-
cyclic submodule of M to M can be extended to M. Let M be a quasi-principally injective …

For a module M and an injective module E over a commutative ring R, we call Hom,(M, E)
the dual of M relative to E [9, Ch. 5, 3 5.41. In [7] L. Melkersson and P. Schenze1 showed …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

We characterize when the direct sum of an extending module and an injective module is
extending and when the direct sum of an extending module with the finite exchange property …