d-n-ideals of commutative rings

Let r be a commutative ring with non-zero identity, and  : i(r) ! i(r) be an ideal expansion where i(r) is the set of all ideals of r. in this paper, we introduce the concept of -n-ideals which is an extension of n-ideals in commutative rings. we call a proper ideal i of r a -n-ideal if whenever a; b 2 r with ab 2 i and a =2 p 0, then b 2 (i). for example, an ideal expansion 1 is dened by 1(i) = p i: in this case, a 1-n-ideal i pis said to be a quasi n-ideal or equivalently, i is quasi n-ideal if i is an n-ideal. a number of characterizations and results with many supporting examples concerning this new class of ideals are given. in particular, we present some results regarding quasi n- ideals. furthermore, we use -n-ideals to characterize elds and un-rings.