It is shown that every pure-injective right module over a ring R is a direct sum of lifting
modules if and only if R is a ring of finite representation type and right local type. In …

A module M over a ring R is called hollow-lifting if every submodule N of M with M/N hollow
contains a direct summand K of M such that N/K is a small submodule of M/K. It is known that …

We introduce Rad-discrete and quasi-Rad-discrete modules as a proper generalization of
(quasi) discrete modules, and provide various properties of these modules. We prove that a …

In this study, inspired by the definition and a previous study [F. Eryılmaz, SS-lifting modules
and rings, Miskolc Math. Notes 22 (2021), no. 2, 655–662], left Harada rings are adapted to …

A module M is called a “lifting module” if, any submodule A of M contains a direct summand
B of M such that A/B is small in M/B. This is a generalization of projective modules over …

Abstract In 1984, Oshiro [11] has studied the decomposition of continuous lifting modules.
He obtained the following: every continuous lifting module has an indecomposable …

In this study, inspired by the definition and a previous study [F. Eryilmaz, SS-lifting modules
and rings, Miskolc Math. Notes 22 (2021), no. 2, 655-662], left Harada rings are adapted to …

The aim of the present article is to investigate the structure of rings R satisfying the condition:
for any family {S i| i∈ ℕ} of simple right R-modules, every essential extension of⊕ i∈ ℕ E (S …

Let R be a right artinian ring or a perfect commutative ring. Let M be a noncosingular self-
generator Σ-lifting module. Then M has a direct decomposition M=⊕< sub> iϵ< sup> IM< …

In this paper we introduce the (∗)-generalized projective modules as a proper
generalization of projective modules. We also investigate the” When is direct sum of two …