When is a BCC-algebra equivalent to an MV-algebra?

• Autorzy: Chajda I. , Halas R. , Kuhr J.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to characterize BCC-algebras which are term equivalent to MV-algebras. It turns out that they arę just the bounded commutative BCC-algebras. Purther, we characterize congruence kernels as deductive systems. The explicit description of a principal deductive system enables us to prove that every subdirectly irreducible bounded commutatwe BCC-algebra is a chain (with respect to the induced order) .

Słowa kluczowe

EN

BCC-algebra; BCK-algebra; MV-algebra

PL

algebra BCC; algebra BCK; algebra MV

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 4
• Strony: 759--768
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Chajda I.

autor

Halas R.

autor

Kuhr J.

• Department of Algebra and Geometry, Palacky University Olomouc Tomkova 40, 779 00 Olomouc, Czech Republic,

Bibliografia

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• [3] I. Chajda and J. Kühr, Algebraic structures derived from BCK-algebras, Miskolc Mathem. Notes, to appear.
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• [5] R. L. O. Cignoli, I. M. L. D'Ottaviano, D. Mundici, Algebraic Foundation of Many-valued Reasoning, Kluwer, Dordrecht-Boston-London, 2000.
• [6] R. Halaš, L. Plojhar, Weakly standard BCC-algebras, J. Mult.-Val. Log. Soft Comput. 12 (2006), to appear.
• [7] Y. Imai, K. Iséki, On axiom systems of propositional calculi, Proc. Japan Acad. 42
• [8] K. Iséki, S. Tanaka, An introduction to the teory of BCK-algebras, Math. Japon. 23 (1978), 1-26.
• [9] Y. Komori, The class of BCC-algebras is not a variety, Math. Japon. 29 (1984), 391-394.
• [10] D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japon. 31 (1986), 889-894.