Residuated lattice congruences via directed kernels

To study the quotient of algebras, like residuated lattices, whose algebraic structures is determined by a partial order, it is often more common to think about directed kernels of homomorphisms between such algebras. So, in this paper, we first introduce the concept of a pre-congruence on a residuated lattice and then characterize them as the directed kernels of the residuated lattice homomorphisms. Second, we characterize the residuated lattice congruences as the intersection of a pre-congruence and its inverse.

Keywords:

Pre-congruence , Residuated lattice congruence , Residuated lattice , quotient