Abstract:

t-norm T of bounded lattices is applied to filters and congruences in residuated lattices, and the concept of TL-filters and TL-congruences of a residuated lattice are introduced. Their properties and some equivalent characterizations are derived.We prove that there is a correspondent bijection between the set of all TL-filters of a residuated lattice and the set of all TL-congruences in that residuated lattice. Finally, quotient residuated lattices and homomorphism theorem are derived. These results and methods still hold in other logical algebraic structures.

Key words: residuated lattices; TL-filters; TL-congruences