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 filter 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 filters 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 filter. Finally, we obtain a characterization of n-fold obstinate filters 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.‎