A representation of symmetric Wajsberg pseudo hoops

This paper explores Wajsberg pseudo hoops derived from filters of bounded Wajsberg pseudo hoops, also known as pseudo MV-algebras. Extending the known result from [1] that every Wajsberg hoop is a maximal filter of an MV-algebra, we introduce symmetric Wajsberg pseudo hoops as a variety encompassing Wajsberg hoops. We demonstrate that every normal filter of a bounded Wajsberg pseudo hoop is an ultrafilter of an appropriate bounded Wajsberg pseudo hoop. Introducing a new binary operation ⊛ on Wajsberg pseudo hoops, we focus on symmetric Wajsberg pseudo hoops. We establish that each such hoop H is isomorphic to the pseudo hoop induced by a filter of a Wajsberg pseudo hoop $A\left(H\right)$, with $A\left(H\right)$ unique up to isomorphism. By analyzing the relationship between normal prime (maximal) filters of H and $A\left(H\right)$, we establish a necessary and sufficient condition for their representability, deepening the understanding of the structural properties of these algebraic systems.