scholarly journals On S-primary submodules

2022 ◽  
pp. 74-89
Author(s):  
H. ANSARI-TOROGHY ◽  
S. S. POURMORTAZAVİ
Keyword(s):  
Primary Submodules

On $n-$absorbing primary submodules

2021 ◽  
Vol Accepted ◽  
Author(s):  
Mohammad Hamoda
Keyword(s):  
Primary Submodules

scholarly journals On intuitionistic L-fuzzy primary and P-primary submodules

2020 ◽  
Vol 8 (4) ◽  
pp. 1417-1426
Author(s):  
Sharma P. K. ◽  
Kanchan K
Keyword(s):  
Primary Submodules

scholarly journals Graded Primary Submodules over Multiplication Modules

2017 ◽  
Vol 225 ◽  
pp. 012079
Author(s):  
Malik Bataineh ◽  
Ala’ Lutfi Khazaaleh
Keyword(s):  
Primary Submodules

scholarly journals On generalizations of classical primary submodules over commutative rings

2018 ◽  
Vol 5 (1) ◽  
pp. 1458556
Author(s):  
P. Yiarayong ◽  
M.  ◽  
Hari M. Srivastava
Keyword(s):  
Commutative Rings ◽  
Primary Submodules

scholarly journals On Generalizations of phi-2-Absorbing Primary Submodules

2018 ◽  
Vol 11 (1) ◽  
pp. 35
Author(s):  
Pairote Yiarayong ◽  
Manoj Siripitukdet
Keyword(s):  
Positive Integer ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Necessary And Sufficient Conditions ◽  
Primary Submodules ◽  
Primary Submodule ◽  
Necessary And Sufficient

Let $\phi: S(M) \rightarrow S(M) \cup \left\lbrace \emptyset\right\rbrace $ be a function where $S(M)$ is the set of all submodules of $M$. In this paper, we extend the concept of $\phi$-$2$-absorbing primary submodules to the context of $\phi$-$2$-absorbing semi-primary submodules. A proper submodule $N$ of $M$ is called a $\phi$-$2$-absorbing semi-primary submodule, if for each $m \in M$ and $a_{1}, a_{2}\in R$ with $a_{1}a_{2}m \in N - \phi(N)$, then $a_{1}a_{2}\in \sqrt{(N : M)}$ or  $a_{1}m \in N$ or $a^{n}_{2}m\in N$, for some positive integer $n$. Those are extended from $2$-absorbing primary, weakly $2$-absorbing primary, almost $2$-absorbing primary, $\phi_{n}$-$2$-absorbing primary, $\omega$-$2$-absorbing primary and $\phi$-$2$-absorbing primary submodules, respectively. Some characterizations of $2$-absorbing semi-primary, $\phi_{n}$-$2$-absorbing semi-primary and $\phi$-$2$-absorbing semi-primary submodules are obtained. Moreover, we investigate relationships between $2$-absorbing semi-primary, $\phi_{n}$-$2$-absorbing semi-primary and $\phi$-primary submodules of modules over commutative rings. Finally, we obtain necessary and sufficient conditions of a $\phi$-$\phi$-$2$-absorbing semi-primary in order to be a $\phi$-$2$-absorbing semi-primary.

On Graded Weakly 2-Absorbing Primary Submodules

2018 ◽  
Vol 47 (2) ◽  
pp. 297-307 ◽  
Author(s):  
Khaldoun Al-Zoubi ◽  
Mariam Al-Azaizeh
Keyword(s):  
Primary Submodules

On graded classical primary submodules

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Khaldoun Al-Zoubi ◽  
Mohammed Al-Dolat
Keyword(s):  
Primary Submodules

AbstractLet

scholarly journals On 2-Absorbing Primary Submodules of Modules over Commutative Rings

2016 ◽  
Vol 24 (1) ◽  
pp. 335-351 ◽  
Author(s):  
Hojjat Mostafanasab ◽  
Ece Yetkin ◽  
Ünsal Tekir ◽  
Ahmad Yousefian Darani
Keyword(s):  
Commutative Rings ◽  
Primary Ideal ◽  
Finitely Generated ◽  
Primary Submodules ◽  
Primary Submodule ◽  
Prime Submodule ◽  
Primary Ideals

Abstract All rings are commutative with 1 ≠ 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a; b ∈ R and m ∈ M and abm ∈ N, then am ∈ M-rad(N) or bm ∈ M-rad(N) or ab ∈(N :R M). It is shown that a proper submodule N of M is a 2-absorbing primary submodule if and only if whenever I1I2K ⊆ N for some ideals I1; I2 of R and some submodule K of M, then I1I2 ⊆ (N :R M) or I1K ⊆ M-rad(N) or I2K ⊆ M-rad(N). We prove that for a submodule N of an R-module M if M-rad(N) is a prime submodule of M, then N is a 2-absorbing primary submodule of M. If N is a 2-absorbing primary submodule of a finitely generated multiplication R-module M, then (N :R M) is a 2-absorbing primary ideal of R and M-rad(N) is a 2-absorbing submodule of M.

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