A module is said to be extending, if every closed (ie complement) submodule is a direct
summand. This property is usually denoted by (Q). It is, obviously, equivalent to the …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

1. Introduction. It is a well-known and basic result of homological alge-bra that the direct
product of an arbitrary family of injective modules over any ring is again injective [3, p. 8] …

We recall that a module is extending if every complement submodule is a direct summand.
In [6] we showed that, over a commutative domain J?, a nontorsion module is extending if …

Rings whose finitely generated modules are extending Page 1 JOURNAL OF PURE AND
Journal of Pure and Applied Algebra 111 (1996) 325-328 APPLIED ALGEBRA Rings whose …

We will say that a module (respectively group) is terse if distinct submodules (respectively
subgroups) are not isomorphic. It is known that a group is terse if and only if it is isomorphic …

It is a well-known result that the direct sum of any family of injective modules over a
Noetherian ring is injective. Conversely, if A is a ring with the property that the direct sum of …

A module is extending (or has the property (Q)) if every complement submodule is a direct
summand. We prove that a module over a commutative domain has this property, if and only …

It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …