n-absorbing I-primary ideals in commutative rings

TL;DR

This paper introduces n-absorbing I-primary ideals as a new generalization in commutative ring theory, exploring their properties and characterizations to deepen understanding of ideal structures.

Contribution

It defines n-absorbing I-primary ideals and investigates their properties, providing new characterizations and conditions for their identification in commutative rings.

Findings

If P is n-absorbing I-primary and √(IP)=I√P, then √P is n-absorbing I-primary.

If √P is (n-1)-absorbing with √(I√P)⊆IP, then P is n-absorbing I-primary.

The paper establishes conditions linking the radicals of ideals to their n-absorbing I-primary status.

Abstract

We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-primary ideals. We investigate some characterizations and properties of such new generalization. If P is an n-absorbing I-primary ideal of R and $\sqrt{IP} =I \sqrt{P} $, then $\sqrt{P}$ is a n-absorbing I-primary ideal of R. Also, if $\sqrt{P}$ is an (n-1)-absorbing ideal of R such that $\sqrt{I \sqrt{P}} \subseteq IP$, then P is an n-absorbing I-primary ideal of R.