Mathematical Logic Quarterly 53 (2):206-213 (2007)

In this paper we prove that the equational class generated by bounded BCK-algebras is the variety generated by the class of finite simple bounded BCK-algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK-algebras is also a relatively simple bounded BCK-algebra. Moreover, we show that every simple bounded BCK-algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class of integral commutative bounded residuated lattices and to the involutive case
Keywords bounded commutative integral residuated lattices  pocrims  semisimple algebras  free algebras  Bounded BCK‐algebras  simple algebras
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DOI 10.1002/malq.200610040
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Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.

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Inconsistency Lemmas in Algebraic Logic.James G. Raftery - 2013 - Mathematical Logic Quarterly 59 (6):393-406.
Lattice BCK Logics with Modus Ponens as Unique Rule.Joan Gispert & Antoni Torrens - 2014 - Mathematical Logic Quarterly 60 (3):230-238.

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