A ring R is semiperfect if and only if, for every (cyclic) R-module M, every maximal
submodule has (ample) supplements in M. A non-local commutative domain R is h-local if …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …

In this note we characterize those commutative rings over which every nonzero module has
a maximal submodule. Professor Hyman Bass in [l, p. 470] states the following conjecture: a …

A module M is called distributive if the lattice Lat (M) of all its submodules is distributive, ie,
Fn (G+ H)= FnG+ FnH for all submodules F, G, and H of the module M. A module M is called …

LetRbe a ring. AnR-moduleM is called a (weak) duo moduleprovided every (direct
summand) submodule of M is fully invariant. It is proved that if R is a commutative domain …

We prove that a module M is cofinitely weak supplemented or briefly cws (ie, every
submodule N of M with M/N finitely generated, has a weak supplement) if and only if every …

A ring will always mean a commutative ring with unit. Let R be a noetherian ring, M a finitely
generated R-module and N a submodule of M. We denote by MinR (M) the set of all minimal …

Abstract A module M satisfies (C< sub> 11</sub>) if every submodule of M has a
complement which is a direct summand of M. It is shown that there exists a commutative …

An R-module M is called principally quasi-injective if each R-hornomorphism from a
principal submodule of M to M can be extended to an endomorphism of M. Many properties …

In this paper we study when a unital right module M over a ring R with identity has a special
“small image” property we call (S*): namely, M has (S*) if every submodule N of M contains a …