On approximately ideals: primary and 1-absorbing ideals in descriptive relator spaces

TL;DR

This paper explores properties of various approximate ideals in descriptive relator spaces, establishing relationships between approx. prime, primary, semi-primary, and 1-absorbing primary ideals, and proving key theorems about their interactions.

Contribution

It introduces the concept of approx. prime ideals and investigates their properties and relationships with other approximate ideals in descriptive relator spaces, providing new theoretical insights.

Findings

If W is an approx.1-absorbing primary ideal, then r(W) is an approx.prime ideal.

An approx.prime ideal W is also an approx.primary ideal.

An approx.prime ideal W is also an approx.1-absorbing primary ideal.

Abstract

For the approx.ideal W of the approx.commutative ring R with unity in a descriptive relator space, after introducing the approx. prime ideal in [], this work demonstrates some special properties of the approx.ideals-specifically, the approx.primary ideal, the approx.semi-primary ideal and the approx.1-absorbing primary ideal. A set of theorems related to these concepts is presented. Among them is this important result: If W is an approx.1-absorbing primary ideal, then r(W) is an approx.prime ideal of the approx. ring R. Furthermore, the relationship between these classes is studied: If W is an approx.prime ideal of R, then W is also an approx.primary ideal. Moreover, it turns out that this is an approx.1-absorbing primary ideal.