Results 41 to 50 of about 466,881 (179)

WE-primary submodules and WE-quasi-prime submodules

Tikrit Journal of Pure Science, 2019
In this paper we introduced and study  two concepts one of is a subclass of a class of weakly primary submodules called WE-primary submodules and the other of a subclass of weakly quasi-prime submodules called WE-quasi-prime submodules.
Haibat K.Mahmmed Ali, Saif A. Hussein
doaj   +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

On Graded φ−Prime Submodules

, 2021
Let $R$ be a graded commutative ring with non-zero unity $1$ and $M$ be a graded unitary $R$-module. Let $GS(M)$ be the set of all graded $R$-submodules of $M$ and $ϕ: GS(M)\rightarrow GS(M)\bigcup\{\emptyset\}$ be a function. A proper graded $R$-submodule $K$ of $M$ is said to be a graded $ϕ-$prime $R$-submodule of $M$ if whenever $r$ is a homogeneous
Alshehry, Azzh Saad, Bataineh, Malik, Abu-Dawwas, Rashid   +2 more
openaire   +2 more sources

Graded I-second submodules

Demonstratio Mathematica, 2021
Let G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1, I be a graded ideal of R, and M be a G-graded R-module. In this article, we introduce the concept of graded I-second submodules of M as a generalization of graded ...
Bataineh Malik, Abu-Dawwas Rashid
doaj   +1 more source

On graded 1-absorbing prime submodules [PDF]

Journal of Discrete Mathematical Sciences and Cryptography, 2021
Let G be a group with identity e, R be a commutative G-graded ring with unity 1 and M be a G-graded unital R-module. In this article, we introduce the concept of graded 1-absorbing prime submodule.
A. Ka'abneh, R. Abu-Dawwas
semanticscholar   +1 more source

A Characterization of Prime Submodules

Journal of Algebra, 1999
Let \(R\) be a commutative ring (with non-zero identity) and let \(M\) be an \(R\)-module. A submodule \(N\) of \(M\) is called prime if \(N\neq M\) and for each \(a\in R\), \(m\in M\), then \(am\in N\) implies \(m\in N\) or \(aM\subseteq N\). Hence if \(N\) is a prime submodule of \(M\), then the annihilator \(\mathfrak p\) of \(M/N\) is a prime ideal
Tiras, Y, Harmanci, A, Smith, PF
openaire   +2 more sources

Approximaitly Primary Submodules

Tikrit Journal of Pure Science, 2019
The study deals with the notion of an approximaitly primary submodules of unitary left -module  over a commutative ring  with identity as a generalization of a primary submodules and approximaitly prime submodules, where a proper submodule  of an ...
Ali Sh. Ajeel, Haibat K. Mohammadali
doaj   +1 more source

WHEN PRIME SUBMODULES ARE PRIME IDEALS?

Mathematical reports, 2022
"We study commutative ring extensions R ⊂ S in which every ideal of S that is a prime R-submodule of S is prime."
Mohamed Khalifa
semanticscholar   +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

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