On weakly (m,n)-closed δ-primary ideals of commutative rings

2022/12/04 by Hamoda, Mohammad, Issoual, Mohammed
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.01916

Abstract

Let R be a commutative ring with 1≠0. In this article, we introduce the concept of weakly (m,n)-closed δ-primary ideals of R and explore its basic properties. We show that I\bowtie^fJ is a weakly (m,n)-closed δ_\bowtie^f-primary ideal of A\bowtie^fJ that is not (m,n)-closed δ_\bowtie^f-primary if and only if I is a weakly (m,n)-closed δ-primary ideal of A that is not (m,n)-closed δ-primary and for every δ-(m,n)-unbreakable-zero element a of I we have (f(a)+j)^m=0 for every j∈~J, where f:A→ B is a homomorphism of rings and J is an ideal of B. Furthermore, we provide examples to demonstrate the validity and applicability of our results.

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