Let A be a right order in a semisimple ring $\Sigma,{M_A} $ be a finite-dimensional
torsionless right A-module and ${\hat M_A} $ be the injective hull of M. JM Zelmanowitz has …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

We study pairs of rings $ R\subset S $ such that $\operatorname {Hom} _R (S,-): R-
\operatorname {Mod}\to S-\operatorname {Mod} $ preserves essential monomorphisms. We …

If R is a maximal two-sided order in a semisimple ring and ${M_R} $ is a finite dimensional
torsionless faithful R-module, we show that $ m={\text {End} _R}\;{M^\ast} $ is a maximal …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

Let (R, M) denote the unitary left module M over the ring R, and let E (R, M) denote the ring
of all R endomorphisms of M. The purpose of this note is to show that the technique used by …

T (M)=(x= M| Hom,(Ra, I (R))= 0) where I (R) is the injective hull of R as a left R-module. A left
R-module M is said to be torsion free if T (M)= 0. For the properties of torsion free modules …

Introduction. The problem considered is a special case of the general problem of the extent
to which a module (F, A) is determined by its endomorphism ring E (F, A). We restrict our …

All rings are associative wit, h identity and all niodules are unitary. Let X be a ring. For a right
R-module Al, E (M) denotes the injective hull of A1 and EndR (M) denotes the …

Let $ R $ be a ring, $ E= E (R_R) $ its injective envelope, $ S=\operatorname {End}(E_R) $
and $ J $ the Jacobson radical of $ S $. It is shown that if every finitely generated submodule …