Algebras on subintervals of pseudo-hoops

If A is a bounded Rℓ-monoid or a pseudo-BL algebra, then it was proved that a subinterval [a,b] of A can be endowed with a structure of an algebra of the same kind as A. Similar results were obtained if A is a residuated lattice and a,b belong to the Boolean center of A. Given a bounded pseudo-hoop A, in this paper we will give conditions for a,b∈A for the subinterval [a,b] of A to be endowed with a structure of a pseudo-hoop. We will introduce the notions of Bosbach and Riečan states on a pseudo-hoop, we study their properties and we prove that any Bosbach state on a good pseudo-hoop is a Riečan state. For the case of a bounded Wajsberg pseudo-hoop we prove that the two states coincide. We also study the restrictions of Bosbach states on subinterval algebras of a pseudo-hoop.