Algebras On Subintervals Of Pseudo-hoops

摘要

If A is a bounded Re-monoid or a pseudo-BL algebra, then it was proved that arnsubinterval [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 Riecan states on a pseudo-hoop, we study their properties and we prove that any Bosbach state on a good pseudo-hoop is a Riecan 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.