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 …

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 …

Extending modules which are direct sums of injective modules and semisimple modules Page 1
COMMUNICATIONS IN ALGEBRA, 24(1 I), 3641-3651 (1996) Extending modules which are …

Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in
case and is finitely generated. We say that M has the property CE (resp. CEE) if M has a …

An R-module M is called∑-extending if every coproduct of copies of M is extending, ie
closed submodules are direct summands. Oshiro (1984) has shown that the ring R is∑ …

We characterize when the direct sum of an extending module and an injective module is
extending and when the direct sum of an extending module with the finite exchange property …

An R-module M is called almost injective if M is a supplement submodule of every module
which contains M. The module M is called F-almost injective if every factor module of M is …

A moduleMis known to be a CS-module (or an extending module) if every complement
submodule ofMis a direct summand. It is shown that (i) a simple ringRmust be right …

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 …

The proof of Theorem 1 can be found in [I, Corollaries 17.4 and 18.81 and [7]. The
equivalence of (i) and (v) is Osofsky's Theorem. This is but one of a number of theorems …