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 paper we provide various properties of Rad-⊕-supplemented modules. In particular,
we prove that a projective module M is Rad-⊕-supplemented if and only if M is⊕ …

We prove that a commutative ring R is an artinian principal ideal ring if and only if the ring is
semilocal and every Rad-supplemented R-module is a direct sum of w-local R-modules …

A left module $ M $ over an arbitrary ring is called an $\mathcal {RD} $-module (or an
$\mathcal {RS} $-module) if every submodule $ N $ of $ M $ with ${\rm Rad}(M)\subseteq N …

Abstract Given modules $ A_ {R} $ and $ _ {R} B $, $ _ {R} B $ is called absolutely $ A_ {R}
$-pure if for every extension $ _ {R} C $ of $ _ {R} B $, $ A\otimes B\rightarrow A\otimes C …

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 …

A submodule N of a right R-module M is said to lie over a direct summand of M if, there is a
decomposition M= M 1⊕ M 2 with M 1⊆ N and N∩ M 2,↪ small M 2. In this paper, a right R …

We introduce⊕-radical supplemented modules and strongly⊕-radical supplemented
modules (briefly, srs⊕-modules) as proper generalizations of⊕-supplemented modules. We …

In generalizing the well-established notion of projective cover, the notions of D3-cover and
rad-projective cover were recently introduced and new characterizations of perfect and …

We define prime uniserial modules as a generalization of uniserial modules. We say that an
R-module M is prime uniserial (℘-uniserial) if its prime submodules are linearly ordered by …