Bounded BCK-algebras and their generated variety

• Autores: J. D. Gispert, Antoni Torrens Torrell
• Localización: Mathematical Logic Quarterly, ISSN 0942-5616, Vol. 53, Nº. 2, 2007, págs. 206-213
• Idioma: inglés
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• Resumen

  • 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. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)