The Decomposition Theorems for Residuated Lattices via Directed Kernels

The isomorphism theorems are those that describe the relationship between quotients, homomorphisms, and subobjects. Also, to construct the quotient of residuated lattices, whose algebraic structures is determined by a partial order, it is more useful to consider directed kernels of homomorphisms between such algebras. So, in this paper, we use the concept of directed kernel of a resituated lattice homomorphism and that of a pre-congruence. Finally, we prove the decomposition and isomorphism theorems for residuated lattice homomorphisms

Keywords:

Pre-congruence , Residuated lattice congruence , Residuated lattice , Decomposition Theorems