info:eu-repo/semantics/article
Factor congruences in BCK-algebras
Fecha
2008-07-29Registro en:
Abad, Manuel; Díaz Varela, José Patricio; Factor congruences in BCK-algebras; Springer Verlag Berlín; Soft Computing; 13; 10; 29-7-2008; 1007-1012
1432-7643
1433-7479
CONICET Digital
CONICET
Autor
Abad, Manuel
Díaz Varela, José Patricio
Resumen
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 of generators is indecomposable in any subvariety 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.