n-Ideals of Commutative Rings

Abstract

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab is an element of I with a is not an element of root 0, then b is an element of I for every a, b is an element of R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.