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N-ideals of commutative rings

Tekir Unsal (Marmara University, Department of Mathematics, Istanbul, Turkey)
Koc Suat (Marmara University, Department of Mathematics, Istanbul, Turkey)
Oral Kursat Hakan (Yildiz Technical University, Department of Mathematics, Istanbul, Turkey)

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  I with a  √0, then b  I for every a,b  R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

Keywords: prime ideal, r-ideal, n-ideal