Results 21 to 30 of about 584 (193)

δ-small submodule and prime modules

, 2023
In this paper, we introduced and studied δ-small submodule over prime module. Two concepts are very important namely strongly prime submodule and completely prime submodule.
Ahmad, Bashaer, Majid Mohammed Abed
core   +1 more source

Strong Essential Submodules And Strong Uniform Modules

Tikrit Journal of Pure Science, 2023
A non-zero submodule K of an R-module M is called essential if K  L  (0)  for each non-zero submodule L of M . And an R-module M is called uniform if each non-zero submodule of M is an essential .
Nada Khalid Abdullah
doaj   +1 more source

(n − 1, n)-weakly prime submodules in direct product of modules [PDF]

Journal of Hyperstructures, 2017
Let n ≥ 2 be a positive integer, R be a commutative ring with identity and M be a unitary R-module . In this paper we study the (n − 1, n)-weakly prime submodules of direct product of modules.
M. Ebrahimpour
doaj   +1 more source

On Prime Submodules

Rocky Mountain Journal of Mathematics, 2007
Throughout \(R\) is a commutative ring with identity. A non-zero module \(M\) is called secondary if for all \(x\in R\), either \(xM=M\) or there exists \(n\in \mathbb{N}\) such that \(x^nM=0\). The authors establish results on secondary modules and on the radicals of a submodule.
Alkan, Mustafa, Tiraş, Yücel
openaire   +2 more sources

t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS [PDF]

Journal of Algebraic Systems
Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$.
Javad Moghaderi, Adnan Tercan
doaj   +1 more source

Nearly Quasi 2-Absorbing submodule

Tikrit Journal of Pure Science, 2023
All rings in this note are commutative rings with identity, and all R modules are left unitary. "A proper submodule E of an R-module X is called nearly quasi prime submodule, if whenever abx ∈ E, with a, b ∈
Haibt K. Mohammadali, Khalaf H Alhabeeb
doaj   +1 more source

φ-PRIME SUBMODULES [PDF]

Glasgow Mathematical Journal, 2009
AbstractLet 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 submodule P of M is a prime submodule relative to φ or φ-prime submodule if a ∈ R and x ∈ M, with ax ∈ P ∖ φ(P) implies that a ∈(P :RM) or x ∈ P. So if we take φ(N)
openaire   +2 more sources

Approximaitly Prime Submodules and Some Related Concepts

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2019
In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity.
Ali Sh. Ajeel, Haibat K. Mohammad Ali
doaj   +1 more source

Weakly Nearly Quasi Prime Submodules

Tikrit Journal of Pure Science, 2022
In this paper, all rings are commutative with identity, and all R-modules are unitary Left R-modules. We introduce the concept WNQP submodule as new generalizations of weakly quasi prime submodule and give basic properties, examples and ...
Hero Jumaa Hassan, Haibat K. Mohammad Ali   +1 more
doaj   +1 more source

WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES [PDF]

Glasgow Mathematical Journal, 2006
A proper submodule N of an R-module M is called a weakly prime submodule, if for each submodule K of M and elements a, b of R, abK ⊆ N, implies that aK ⊆ N or bK ⊆ N. In this paper we will study weakly prime submodules and we shall compare weakly prime submodules with prime submodules.
openaire   +1 more source