\((m, n)\)-closed \(\delta \)-primary ideals in amalgamation
type: Item
instance of: scholarly article
title: \((m, n)\)-closed \(\delta \)-primary ideals in amalgamation
author: Mohammad Hamoda
author: Mohammed Issoual
published in: Communications of the Korean Mathematical Society
publication date: 2024-10-10T00:00:00Z
review text: Let \(R\) be a commutative ring with \(1\neq 0\). Let \(Id(R)\) be the set of all ideals of \(R\) and let \(\delta: Id(R)\longrightarrow Id(R)\) be a function. Then \(\delta\) is called an expansion function of the ideals of \(R\) if whenever \(L, I, J\) are ideals of \(R\) with \(J\subseteq I,\) then \(L\subseteq \delta(L)\) and \(\delta(J)\subseteq \delta(I)\). Let \(\delta\) be an expansion function of the ideals of \(R\) and \(m\geq n \ge 0\) be positive integers. Then a proper ideal \(I\) of \(R\) is called an \((m,n)\)-closed \(\delta\)-primary ideal (resp., weakly \((m,n)\)-closed \(\delta\)-primary ideal) if \(a^m \in I\) for some \(a\in R\) implies \(a^n\in \delta(I)\) (resp., if \(0\neq a^m\in I\) for some \(a\in R\) implies \(a^n \in \delta(I))\). Let \(f: A\longrightarrow B\) be a ring homomorphism and let \(J\) be an ideal of \(B\). This paper investigates the concept of \((m, n)\)-closed \(\delta\)-primary ideals in the amalgamation of \(A\) with \(B\) along \(J\) with respect to \(f\).
reviewed by: T. Tamizh Chelvam
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13E99
zbMATH DE Number: 7924502
zbMATH Keywords: \( \delta \)-primary ideal
zbMATH Keywords: \((m, n)\)-closed \(\delta \)-primary ideal
zbMATH Keywords: weakly \((m, n)\)-closed \(\delta \)-primary ideal
zbMATH Keywords: amalgamation
zbMATH Keywords: trivial extension
MaRDI profile type: Publication
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DOI: 10.4134/CKMS.C230266
description: scientific article; zbMATH DE number 7924502