Minimal prime ideals in hoops

Document Type : Original Article


1 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University

2 Hatef University


In this paper, we define the notion of minimal prime ideals of hoops and investigate some properties of them. Then by using the notion of annihilators, we study the relation between minimal prime ideals and annihilators. Also, we introduce the notion of zero divisors elements of hoops and prove that the set of all zero divisors of hoops is a union of all minimal prime ideals of hoop. Finally, by using the notions of minimal prime ideals and maximal ideals of hoop, we introduce two new ideals as p-ideal and m-ideal. Then we study some properties of them and investigate the relation between them and prove that every p-ideal of semi-simple hoop is an m-ideal of it.