Semistar operations on conductive domains

(S3)E⊆E★ and (E★)★=E★. We shall denote the set of semistar operations (resp. the set of star operations) on D by SStar (D) (resp. Star (D)) as in [5]. The main purpose of this paper is to investigate semistar operations on conducive domains. We also study the number of semistar operations. We shall denote the cardinality of a set X by |X| and the symbol⊂means "proper inclusion" . Throughout this paper, D denotes an integral domain with quotient field K and D the integral closure of D. Furthermore we always assume D≠K. Any unexplained terminology is standard, as in [7].