A proper submodule N of an R-module M is called a weakly prime [resp. a prime]
submodule, if for any elements a, b∈ R and x∈ M, the condition abx∈ N [resp. ax∈ N] …

Let R be a commutative unital ring and a ∈ R. a∈ R. We introduce and study properties of a
functor a Γ _ a (-), a Γ a (-), called the locally nilradical on the category of R-modules. a Γ _ a …

In this article, we introduce new classes of submodules called $ r $-submodule and special
$ r $-submodule, which are two different generalizations of $ r $-ideals. Let $ M $ be an $ R …

Let B be a submodule of an R-module M. The intersection of all prime (resp. weakly prime)
submodules of M containing B is denoted by rad (B)(resp. wrad (B)). A generalisation of< E …

PRIME SUBMODULES OF ARTINIAN MODULES Page 1 TAIWANESE JOURNAL OF
MATHEMATICS Vol. 13, No. 6B, pp. 2011-2020, December 2009 This paper is available online at …

Let $ k $ be a field with characteristic zero, $ R $ be the ring $ k [x_1,\cdots, x_n] $ and $ I $
be a monomial ideal of $ R $. We study the Artinian local algebra $ R/I $ when considered …

This article, in view of the connection between S-acts and modules, is devoted to the study
some properties of prime and primary subacts. Moreover, the notions of second and …

Let R be a commutative ring with identity. We will say that an R-module M has Nakayama
property, if IM= M, where I is an ideal of R, implies that there exists a∈ R such that aM= 0 …

ARITHMETICAL RINGS SATISFY THE RADICAL FORMULA 1. Introduction. Throughout this
article, rings are assumed to be commutative wit Page 1 JOURNAL OF COMMUTATIVE …

Let $ R $ be a commutative unital ring and $ N $ be a submodule of an $ R $-module $ M $.
The submodule $\langle E_M (N)\rangle $ generated by the envelope $ E_M (N) $ of $ N …