On a new construction of pseudo BL-algebras

We present a new construction of a class of pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop. Using two injective mappings from one set into the second one, and an identical copy of the basic pseudo hoop with the reverse order we construct a pseudo BL-algebra. We show that such a structure is a pseudo BL-algebra iff the basic pseudo hoop is cancellative. Starting with a commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification.