Some results on ϕ-primary submodules

Document Type : Research Paper

Authors
Mohammad Hosein Moslemi Koopaei 1
Masoud Zolfaghari 2
1 Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran
2 Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran
10.22075/ijnaa.2024.33810.5051
Abstract
Let $R$ be a commutative ring with identity,  $M$ be an unitary $R$-module, let $\mathcal{S}(M)$ be the set of all submodules of $M$ and $\phi : \mathcal{S}(M)\rightarrow \mathcal{S}(M)\cup \lbrace\emptyset\rbrace$ be a function. A proper submodule $N$ of $M$ is called $\phi$-pimary submodule if $rx\in N \setminus \phi(N)$ where $r\in R$ and $x\in M$, implies that $x\in N$ or $r\in \sqrt{(N:M)}$. In this work, $\phi$-primary submodules are studied, and some results are obtained.
Keywords
ϕ-prime ideal
ϕ-primary ideal
ϕ-prime submodule
ϕ-primary submodule
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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 10
October 2025
Pages 125-129

  • Receive Date 22 April 2024
  • Accept Date 26 May 2024