TL-filters and TL-congruences of residuated lattices
Xiaoyan Qin · Journal of Shandong University · 2012
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.