Hiroki TAKAMURA EVERY FREE BIRESIDUATED LATTICE IS SEMISIMPLE
نویسنده
چکیده
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 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 Grǐsin’s idea in [2]. We show that their proof of the semisimplicity works well also for free biresiduated lattices.
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