Factor Congruences in BCK algebras

ABAD MANUEL; DÍAZ VARELA JOSÉ PATRICIO

Soft Computing

Springer

Año: 2008 vol. 13 p. 1003 - 1012

1432-7643

Abstract In this paper, we characterize factor congruences ,  in the quasivariety of BCK-algebras. As an application we ,  prove that the free algebra over an infinite set ofgenerators ,  is indecomposable in anysubvariety of BCK-algebras. We ,  also study the decomposability of free algebras in the variety ,  of hoop residuation algebras (HBCK)and its subvarieties. ,  We prove that free algebras in a non k-potent subvariety ,  of HBCK are indecomposable while finitely generated free ,  algebras in k-potent subvarieties have a unique non-trivial ,  decomposition into a direct product of two factors, and one ,  of them is the two-element implication algebra. ,