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Varieties generated by finite BCK-algebras

Published online by Cambridge University Press:  17 April 2009

William H. Cornish
William H. Cornish
Affiliation:
School of Mathematical Sciences, Flinders University, Bedford Park, South Australia 5042, Australia.
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Abstract

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Iséki's BCK-algebras form a quasivariety of groupoids and a finite BCK-algebra must satisfy the identity (En): xyn = xyn+1, for a suitable positive integer n. The class of BCK-algebras which satisfy (En) is a variety which has strongly equationally definable principal congruences, congruence-3-distributivity, and congruence-3-permutability. Thus, a finite BCK-algebra generates a 3-based variety of BCK-algebras. The variety of bounded commutative BCK-algebras which satisfy (En) is generated by n finite algebras, each of which is semiprimal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 3 , December 1980 , pp. 411 - 430
Copyright
Copyright © Australian Mathematical Society 1980

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