A ring R is said to be left n-semihereditary, if every n-generated left ideal of R is projective. It
is shown that for a ring R, the following statements are equivalent:(1) R is left n …

In this paper, the concepts of quasi-c-principally injective modules (in short, quasi-cp-
injective modules) and self-c-principally injective rings are introduced. In support of these …

Let $ n, d $ be two non-negative integers. A left $ R $-module $ M $ is called $(n, d) $-
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A …

In this paper, the concepts of SGQ-projective, quasi-epi-projective and quasi-epi-projective
modules are introduced and some properties of these modules are investigated. Hopfian …

Apstract. Let be a ring with identity and let be a left R-module. is called J-semiregular
module if every cyclic submodule of is J-lying over a projective summand of, The aim of this …

This study presents a semi-quasi Hamsher module that each non-zero Artinian submodule
has a semi-maximal submodule, which is a generalized of Hamsher module. And semi …

Let M be a left R− module. In this paper, various results pertaining to the equivalence of
discrete modules and pseudo-discrete modules are established. Furthermore, a new class …

A ring R is left co-semihereditary (strongly left co-semihereditary) if every finitely
cogenerated factor of a finitely cogenerated (arbitrary) injective left R-module is injective. A …

An R-module M is called polyform if every essential submodule of M is rational. The main
goal of this paper is to give a new class of modules named P-polyform modules. This class …

Let R be a ring with identity and M be a right unitary R-module. In this paper we introduce
the notion of strongly coretractable modules. Some basic properties of this class of modules …