Let R be a ring and 𝒲 a self-orthogonal class of left R-modules which is closed under finite
direct sums and direct summands. A complex C of left R-modules is called a 𝒲-complex if it …

Direct complements in a right R-module M are said to be almost unique if, whenever M= A⊕
B= A⊕ C, then (B+ C)/B≪ M/B (also (B+ C)/C≪ M/C, by symmetry). We will show that this …

Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of
S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator ann M n …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

In this paper, we obtain that a commutative ring R is w-coherent if and only if Hom R (M, E) is
w-flat for any absolutely pure w-module M and any injective (w-) module E, if and only if Hom …

Keskin and Harmanci defined the family B (M, X)= ${A {\leq} M|{\exists} Y {\leq} X,{\exists} f
{\in} Hom_R (M, X/Y),\; Ker\; f/A {\ll} M/A} $. And Orhan and Keskin generalized projective …

The focus of this paper are essential submodules, A, of the maximal right ring of quotients,
Qr R, of a right non-singular ring R. Since Qr is a RR-bimodule, particular attention is given …

I t is proved that if R is a right Coldie ring which satisfies dcc on right annihilators and if n is a
positive integer such that every finitely generated free right R-module satisfies acc on n …

CORRESPONDENCES OF CLOSED SUBMODULES There is a considerable body of research
dealing with correspondences between the lattice o Page 1 PROCEEDINGS OF THE AMERICAN …

In this paper we study (non-commutative) rings $ R $ over which every finitely generated left
module is a direct sum of cyclic modules (called left FGC-rings). The commutative case was …