On residuated skew lattices

Abstract

In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s relation 𝔻 is a congruence relation on residuated skew lattice and its quotient algebra is a residuated lattice. Deductive system and skew deductive system in residuated skew lattices are defined and relationships between them are given and proved. We define branchwise residuated skew lattice and show that a conormal distributive residuated skew lattice is equivalent with a branchwise residuated skew lattice under a condition.

Keywords

• skew lattice
• residuated lattice
• residuated skew lattice
• green’s relation
• variety
• (skew) deductive system
• primary 03g10
• secondary 06a75, 06b20