A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

Lomp [9] has studied finitely generated projective modules over semilocal rings. He
obtained the following: finitely generated projective modules over semilocal rings are …

The purpose of this paper is to initiate the study of improjective modules. A module X is im-
projective if given any epimorphism/: B-> A and any homomorphism/: X-> A, there exists a …

The purpose of this paper is to introduce new concepts in a module over a ring, the first one
is called e*-small essential submodule, which is a generalization of the small submodule …

In this paper, we introduce the notion of finite direct projective modules, which is a
generalization of direct projective modules; counter-example is given. We study the …

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 …

A module M is called virtually semisimple (resp. virtually extending) if every submodule
(resp. complement submodule) of M is isomorphic to a direct summand of M. It is known that …

d-Small Submodules and d-Small Projective Modules Page 1 International Journal of
Algebra, Vol. 12, 2018, no. 1, 25 - 30 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2018.71045 …

This is a study of the conditions under which smallness of proper submodules will influence
the structure of the endomorphism ring of a module. The case in which that endomorphism …

A fully invariant submodule of is called fully prime in if for fully invariant submodules and of,
implies or with. In this paper, we give some characterizations of fully prime submodules. We …