Hiroki TAKAMURA:
Every Free Biresiduated Lattice is Semisimple
A b s t r a c t. In this paper, we prove the semisimplicity of free biresiduated lattices, more precisely, integral residuated
lattices. In [4], authors show that variety of residuated lattices, more precisely, commutative integral residuated
lattices, is generated by its finite simple members. The result is obtained by showing that every {\it free} residuated lattice is
semisimple and then showing that every variety generated by a simple residuated lattice is generated by a set of finite simple
residuated lattices. The proof of the former is based on Gri\v{s}in's idea in [2]. We show that their proof of the
semisimplicity works well also for free biresiduated lattices.