S(0)-IDEALS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with nonzero identity, let 1 ( R ) be the set of all ideals of R and S : 1 ( R )-* 1 ( R ) be a function. Then S is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J C I , we have L C S ( L ) and S ( J ) C S ( I ). In this paper, we present the concept of S (0)-ideals in commutative rings. A proper ideal I of R is called a S (0)-ideal if whenever a , b E R with ab E I and a E/ S (0), we have b E I . Our purpose is to extend the concept of n-ideals to S (0)-ideals of commutative rings. Then we investigate the basic properties of S (0)-ideals and also, we give many examples about S (0)-ideals.