In this article, a new radical formula for a module over a commutative ring is introduced by
constructing a generalization of radical and envelope and defining an (e, r)-radical formula …

A closure operation on submodules 1. Introduction Throughout the paper, R is a commutative ring
with nonzero identity, all modul Page 1 Journal of Algebra and Its Applications Vol. 16, No. 12 …

In this paper, we introduce and study some new generalizations of second submodules via a
function φ on the set of all submodules of a module. Let R be a ring with non-zero identity, M …

Let R be a commutative ring with identity, M be an R-module, n≥ 2 be a positive integer and
ϕ: S (M)−→ S (M) be a function where S (M) is the set of all submodules of M. In this paper …

Let R be a commutative ring with identity and M be a unital R-module. Let S (M) be the set of
all submodules of M and φ: S (M)→ S (M)∪{∅} be a function. We define a proper submodule …

absorbing submodule is generalization of the notion of 2-absorbing ideal. We will study 2-
absorbing submodules and we prove that 2-absorbing submodules are not too far from …