  In this paper, the notions of integral closure of hyperrings and hyperideals
in a Krasner hyperring $(R, +, \cdot)$ are defined and some basics properties
of them are studied. We define also the notion of hypervaluation hyperideals
and then a relations between hypervaluations, integral closure of hyperideals
and primary hyperideals are studied. In fact it is shown that the integral
closure of a hyperideal is determined by the hypervaluation Krasner hyperrings.
