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Bounded BCK-algebras and their generated variety

✍ Scribed by Joan Gispert; Antoni Torrens

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
170 KB
Volume
53
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

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)

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