One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition,
where a module M is called a C3-module if whenever A and B are direct summands of M …

An R-module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with
M= A 1⊕ A 2 and f: A 1→ A 2 is an R-homomorphism with ker f⊆⊕ A 1, we have I mf⊆⊕ A …

In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

Introduction. In [5] it is left as a question whether direct sums and summands of weak CS-
modules are weak CS or not. Some particular answers are given to the former question in [5 …

We define and investigate T 11-type modules as a generalization of t-extending modules,
and modules satisfying C 11 condition. A module M is said to be T 11-type if every t-closed …

Let R be a ring and let M= M•© M2 be a right R-module which is the direct sum of
submodules M•, M2. We are interested in conditions on M•, M2 which make M a CS-module …

It is well known that if every cyclic right module over a ring is injective, then the ring is
semisimple artinian. This classical theorem of Osofsky promoted a considerable interest in …

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 over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

Let R be a ring with identity and M be an R-module with unity. In this paper we introduce the
notion of C-coretractable modules. Some basic properties of this class of modules are …