The concept of the M-radical of a submodule B of an R-module A is discussed (R is a
commutative ring with identity and A is a unitary fl-module). The M-radical of B is defined as …

If R is a commutative ring with identity, then the radical of a primary ideal of R is a prime
ideal of R. We will try to study and generalize this property to modules. It is proved that if one …

Throughout this paper, $ R $ is an associative ring (not necessarily commutative) with
identity and $ M $ is a right $ R $-module with unitary. In this paper, we introduce a new …

Let R be a commutative ring with identity and M be an unitary R-module. Let(M) bethe set
of all submodules of M, and:(M)(M){} be a function. We say that aproper …

In this paper we study weakly prime submodules of a module over a commutative ring with
identity. First, a number of results concerning weakly prime submodules are given. Second …

On Semi-Essential Subsemimodules in Multiplication Semimodules Page 1 ISSN 2347-1921
Volume 12 Number 07 Journal of Advances in Mathematics 6449 | Page council for Innovative …

We will introduce and study the notion of prime bases for weakly prime submodules and
utilize them to derive some formulas on the weak radical of submodules of a module. In …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …

Let R be a commutative ring with identity and let M be an R-module. Then M is called a
multiplication module if for every submodule N of M there exists an ideal I of R such that N …

In this paper the definition of an...-weak multiplication module is given and we prove some
results for such a module. Then, using the definition of a semiprime submodule of a module …