This paper give a new fact about the extending module. A module M is called extending if
every closed submodule N of M is a direct summand. Study of the concepts complement …

In this note we consider a generalization of the notion of extending modules namely
supplement extending modules. And study the relation between extending and supplement …

In this work, we introduce a new generalization of both Rationally extending and Goldie
extending which is Goldie Rationally extending module which is known as follows: if for any …

The goal of this research is to introduce the concepts of Large-small submodule and Large-
hollow module and some properties of them are considered, such that a proper submodule …

Let 𝑅 be a commutative ring with 1 and 𝑀 be a left unitary 𝑅− 𝑚𝑜𝑑𝑢𝑙𝑒. In this paper, the
generalizations for the notions of compressible module and retractable module are given …

In this paper, principally quasi injective system has been introduced and studied, which is a
generalization of quasi injective system. We obtain a characterizations of PQ-injective …

The notion of rationally-extending module and supplement submodule are known. In our
work, we introduce a supplement rationally-extending module," which is a proper …

Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce
the concept small monoform module as a generalization of monoform module. A module M …

Given a Banachspace 𝐸 is aBanach left 𝐴-module if 𝐸 is a left 𝐴− module, and‖ 𝑎. 𝑥‖≤‖
𝑎‖‖ 𝑥‖(𝑎∈ 𝐴, 𝑥∈ 𝐸)[1]. Recall that a submoduleN of an 𝑅− module 𝑀 is said to be …

In this paper, we introduce the notions of strongly t-semisimple modules and strongly t-
semisimple rings as a generalization of semisimple modules, rings respectively. We …