Abstract:

The ideals in residuated lattice are studied. Some properties of ideals are given, and a congruence relation is structured based on the notion of ideals in residuated lattice. It is proved that the quotient algebra of a residuated lattice under this congruence relation is also a residuated lattice. Some characterization theories of ideals in regular residuated lattice are obtained.

Key words: residuated lattices; regular residuated lattices; ideals; congruence relation; characterization theory