Pseudo-equality Algebras and Residuated Posets
In this paper, we study the relationship between pseudo-equality algebras and quantum B-algebras and the relationship between pseudoequality algebras and residuated posets. Also, we present some properties of residuated posets and get a one-to-one correspondence between the congruences and normal filters in a residuated poset. We introduce the notion of implicative filters of a residuated poset and characterize these filters. Moreover, we investigate implicative homomorphisms of residuated posets and obtain the homomorphism theorem.
Keywords: Pseudo-equality algebra, residuated poset, quantum B-algebra, BCK-algebra, implicative semigroup