Let 𝑅 be a commutative ring with identity, and let 𝑀 be a unital 𝑅-module. A submodule 𝑁 of
𝑀 is called a dense submodule, if 𝑀=∑ 𝜑𝜑 (𝑁) where 𝜑 runs over all the 𝑅-morphisms from …

Modules in which every proper submodule (resp. proper nonzero submodule) is prime
(called fully prime (almost fully prime)) and with some other related notions are fully …

Let R be a commutative ring with identity and M a unitary R-module. Some properties of
prime submodules of an R-module M have been discussed. In this paper, we investigate the …

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let (M) be
the set of all submodules of M, and φ:(M)→(M)∪{∅} be a function. We say that a proper …

‎ Let $ R $ be a commutative ring with identity‎,‎ $ S $ a multiplicatively closed subset of $ R $‎,‎
and $ M $ be an $ R $-module‎.‎ The goal of this work is to introduce the notion of $ S $-pure …

Modules over strongly prime rings Page 1 Journal of Algebra and Its Applications Vol. 14, No. 5
(2015) 1550076 (9 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219498815500760 …

Let $ R $ be a commutative ring with identity and $ M $ be a unitary $ R $-module. A
submodule $ N $ of $ M $ is called a dense submodule if ${\rm {Hom}} _R (M/N, E_R (M)) …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

Let R be a commutative ring with non-zero identity. We define a proper submodule Nof an R-
module M to be quasi-primary if PM Nrad R=):(is a prime ideal of R. In this case we also say …