d-n-ideals of commutative rings

Let R be a commutative ring with non-zero identity, and \delta :\mathcal{I(R)}\rightarrow\mathcal{I(R)} be an ideal expansion where \mathcal{I(R)} is the set of all ideals of R. In this paper, we introduce the concept of \delta-n-ideals which is an extension of n-ideals in commutative rings. We call a proper ideal I of R a \delta-n-ideal ifwhenever a,b\in R with\ ab\in I and a\notin\sqrt{۰}, then b\in \delta(I). For example, an ideal expansion \delta_{۱} is defined by \delta_{۱}(I)=\sqrt{I}. In this case, a \delta_{۱}-n-ideal I is said to be a quasi n-ideal or equivalently, I is quasi n-ideal if \sqrt{I} is an n-ideal. A number of characterizations and results with manysupporting examples concerning this new class of ideals are given. In particular, we present some results regarding quasi n-ideals. Furthermore, we use \delta-n-ideals to characterize fields and UN-rings.

کلیدواژه ها:

delta-n-ideal ، quasi n-ideal ، n-ideal ، delta-primary ideal