The New Generalization of Wajsberg Algebras
Wenjuan Chen
This paper investigates a new generalization of Wajsberg algebras, called quasi-pseudo-Wajsberg algebras. Such algebras also generalize both pseudo-Wajsberg algebras and quasi-Wajsberg algebras. First we discuss some properties related to the lattice-like structures of quasi-pseudo-Wajsberg algebras. And then we prove that quasi-pseudo-Wajsberg algebras are equivalent to quasi-pseudo-MV algebras. Finally, we characterize the equivalent relations between quasi-pseudo-Wajsberg algebras and some residuated semigroups.
Keywords: Wajsberg algebras; pseudo-Wajsberg algebras; quasi-Wajsberg algebras; quasi-pseudo-MV algebras; quasi-pseudo-Wajsberg algebras; DRl-monoids