$\delta$-$n$-ideals of commutative rings

Let $R$ be a commutative ring with nonzero identity, and $\delta :$\mathcal{I}(\mathcal{R})$\rightarrow$\mathcal{I}(\mathcal{R})$$beanidealexpansionwhere$$\mathcal{I}(\mathcal{R})$$thesetofallidealsof$R$. 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 if whenever $a,b\in R$ with$ab\in I$ and $a\mathrm{\notin }\sqrt{0}$, then $b\in \delta(I)$\mathrm{.}Forexample,$\delta_{1}$isdefinedby$\delta_{1}(I)=\sqrt{I}.$ A number of results and characterizations related to $\delta$-$n$-ideals are given. Furthermore, we present some results related to quasi $n$-ideals which is for the particular case $\delta ={\delta }_1\mathrm{.}$