Let M be a right R− module. A right R− module N is called small pseudo principally M−
injective (briefly, small PP M−− injective) if, every R− monomorphism from a small and …

For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed
by M, the endomorphism ring E formed by AMB⊗, and the endomorphism ring F formed by …

A characterization is given of when all kernels (respectively images) of endomorphisms of a
module are direct summands, a necessary condition being that the endomorphism ring itself …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

Let R be a ring, K, M be R-modules, L a uniserial R-module, and X a submodule of L. The
triple (K, L, M) is said to be X-sub-exact at L if the sequence K→ X→ M is exact. Let σ (K, L …

Let $ R $ be a ring and $ S $ a multiplicative subset of $ R $. An $ R $-module $ T $ is called
$ u $-$ S $-torsion ($ u $-always abbreviates uniformly) provided that $ sT= 0$ for some …

On projective modules with semilocal endomorphims ring. Page 1 On projective modules with
semilocal endomorphims ring. C. Lomp, M. Nasrutdinov and I. Sakhaev October 21, 2010 …

The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

A module A is called principally self injective if for each principal left ideal L of R and each
homomorphism f: L−→ A with kerf⊇ ann (a) for some a∈ A, there is a homomorphism R−→ …

We say that a ring K is (right) split by a subring A provided that A is an (right) A-module direct
summand of K. Then K is said to be a split extension of A. By a theorem of Azumaya [lJ, a …