n-fold obstinate filters in pseudo-hoop algebras

In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate lter in pseudo-hoops. then we investigated these notions and proved some properties of them. also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold fllters such as n-fold(positive) implicative filter and n-fold fantastic filter in pseudo-hoops. for example, we proved that any n-fold obstinate filter is a maximal lter. finally, we obtain a characterization of n-fold obstinate lters in terms of congruences and we show that any n-fold obstinate pseudo-hoop is an n-fold fantastic, n-fold positive implicative, n-fold implicative pseudo-hoop and simple pseudo-hoop.