Factor congruences in BCK-algebras

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...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 13; no. 10; pp. 1007 - 1012
Main Authors Abad, Manuel, Díaz Varela, J. Patricio
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.08.2009
Springer Nature B.V
Subjects
Algebra
Artificial Intelligence
Computational Intelligence
Congruences
Control
Decomposition
Engineering
Mathematical Logic and Foundations
Mechatronics
Original Paper
Robotics
Hoops
Implicative filters
Pocrims
Decomposability
Factor congruences
algebras
Free algebras
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Summary: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 and its subvarieties. We prove that free algebras in a non k -potent subvariety of 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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-008-0346-4