Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …

Let $ R $ be any ring and let $ M $ be any right $ R $-module. $ M $ is called hollow-lifting if
every submodule $ N $ of $ M $ such that $ M/N $ is hollow has a coessential submodule …

A module M is⊕‐supplemented if every submodule of M has a supplement which is a direct
summand of M. In this paper, we show that a quotient of a⊕‐supplemented module is not in …

We introduce the notions of “t-extending modules,” and “t-Baer modules,” which are
generalizations of extending modules. The second notion is also a generalization of …

Let R be a ring and M a right R-module. M is called⌖-supplemented if every submodule of M
has a supplement that is a direct summand of M, and M is called completely⌖-supplemented …

An R-module M is called an extending module, and also called CS, if it satisfies the following
full extending property: For any submodule X of M, there exists a direct summand X∗ of M …

A module M is called extending if every submodule of M is essential in a direct summand.
We call a module FI-extending if every fully invariant submodule is essential in a direct …

Absolutely pure modules act in ways similar to injective modules. There are conditions on a
ring which guarantee that the class of injective modules will be covering. In this article, we …

Modules which are extending relative to module classes Page 1 COMMUNICATIONS IN
ALGEBRA, 26(6), 1699- 172 1 (1998) MODULES WHICH ARE EXTENDING RELATIVE TO …

Throughout this paper we assume that all modules are finitely generated (left) modules over
a noetherian R-algebra A for a commutative local ring R. By a noetherian R-algebra A, we …