Abstract A module\(M\) is said to be lifting if, for any submodule\(N\) of\(M\), there exists a
direct summand\(X\) of\(M\) contained in\(N\) such that\(N/X\) is small in\(M/X\). A module\(M\) …

Modules Whose h-Closed Submodules Are Direct Summands Page 1 Southeast Asian Bulletin of
Mathematics c SEAMS. 2020 Southeast Asian Bulletin of Mathematics (2020) 44: 79–86 Modules …

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∑ …

In the second section we shall deal with more general rings than sl: rial rings defined by
Nakayama [lo]. He showed that if a ring R is a serial ring, 1; hen every finitely generated …

A module M is called closed weak supplemented if for any closed submodule N of M, there
is a submodule K of M such that M= K+ N and K∩ N<< M. Any direct summand of closed …

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 …

This paper introduced a new generalization of extending modules, namely modules in which
every closed full large extension of a cyclic submodule is a direct summand, introduced a …

Throughout this paper R represents commutative ring with identity, and M is a unitary left R-
module. The purpose of this paper is to study a new concept,(up to our knowledge), named …

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 …