Generalised lattice ordered groupoids (gl – groupoids)

Abstract: This paper, deals with the concept of gl-groupoid in such a way that every l-groupoid is a gl-groupoid but not conversely. The concepts of gl-semigroup, gl-monoid, residuated generalised lattice and integral gl-groupoid have been identified.. and also Galois connection on a residuated generalised lattice is established. Proved that a complemented integral gl-groupoid satisfying some condition is distributive