Archive for Mathematical Logic 45 (8):1011-1020 (2006)

Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be only decomposed into a direct product of two factors, one of which is the two-element implication algebra
Keywords Free algebras  Factor congruences  Implicative filters  BCK-algebras  MV-algebras
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DOI 10.1007/s00153-006-0023-1
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References found in this work BETA

Semi-Boolean Algebra.[author unknown] - 1972 - Journal of Symbolic Logic 37 (1):191-191.

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Free Łukasiewicz Implication Algebras.José Patricio Díaz Varela - 2008 - Archive for Mathematical Logic 47 (1):25-33.

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