S-principal ideal multiplication modules

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Aslankarayiğit Uğurlu E., Koç S., Tekir Ü.

COMMUNICATIONS IN ALGEBRA, vol.51, no.5, pp.1-10, 2023 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 51 Issue: 5
• Publication Date: 2023
• Doi Number: 10.1080/00927872.2022.2164772
• Journal Name: COMMUNICATIONS IN ALGEBRA
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
• Page Numbers: pp.1-10
• Marmara University Affiliated: Yes

Abstract

In this paper, we study S-Principal ideal multiplication modules. Let A " role="presentation" >A $A$ be a commutative ring with 1≠0, S⊆A" role="presentation" >1≠0, S⊆A$1\ne 0,S\subseteq A$ a multiplicatively closed set and M " role="presentation" >M $M$ an A-module. A submodule N of M is said to be an S-multiple of M if there exist s∈S" role="presentation" >s∈S$s\in S$ and a principal ideal I of A such that sN⊆IM⊆N" role="presentation" >sN⊆IM⊆N$sN\subseteq IM\subseteq N$. M " role="presentation" >M $M$ is said to be an S-principal ideal multiplication module if every submodule N " role="presentation" >N $N$ of M " role="presentation" >M $M$ is an S-multiple of M. Various examples and properties of S-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extension A⋉M" role="presentation" >A⋉M$A⋉M$ is an S⋉0" role="presentation" >S⋉0$S⋉0$-principal ideal ring. Also, we prove Cohen type theorem for S-principal ideal multiplication modules in terms of S-prime submodules.