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

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.