Integral closures, primary hyperideals and hypervaluation hyperideals of Kranser hyperrings

In this paper, the notions of integral closure of hyperrings and hyperideals in a Krasner hyperring (R, +, .) 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.