‎ 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 …

Fully prime rings (in which every proper ideal is prime) have been studied by Blair and
Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been …

Abstract. Let R be a commutative ring with identity and let M be a unital R-module. In this
paper we study the various properties of prime submodules. Also we give a new equivalent …

Let $ R $ be a commutative ring with identity and $ M $ be a unital $ R $-module. A proper
submodule $ N $ of $ M $ with $ N: _RM=\frak p $ is said to be prime or $\frak p $-prime …

Acta Mathematica Academiae Paedagogicae Nyıregyháziensis 33 (2017), 165–173 www.emis.de/journals
ISSN 1786-0091 I-PRIME SUBM Page 1 Acta Mathematica Academiae Paedagogicae …

A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

Let R be a ring and M a right R‐module. It is shown that (1) δ (M) is Noetherian if and only if
M satisfies ACC on δ‐small submodules;(2) δ (M) is Artinian if and only if M satisfies DCC on …

The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

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 …

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 is an element …