Distributive implication groupoids

• Autorzy: Ivan Chajda , Radomir Halaš
• Języki publikacji: EN

Abstrakty

EN

We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.

Słowa kluczowe

EN

(distributive) implication groupoid; ideal; deductive system; congruence kernel; left distributivity

Kategorie tematyczne

• 20N02: Sets with a single binary operation (groupoids)
• 06F35: BCK-algebras, BCI-algebras
• 08A30: Subalgebras, congruence relations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 484-492

Daty

wydano

2007-09-01

online

2007-09-01

Twórcy

autor

Ivan Chajda

• Palacký University Olomouc Tomkova 40

autor

Radomir Halaš

• Palacký University Olomouc Tomkova 40

Bibliografia

• [1] J.C. Abbott: “Semi-boolean algebra”, Matem. Vestnik, Vol. 4, (1967), pp. 177–198.
• [2] I. Chajda and R. Halaš: “Algebraic properties of pre-logics”, Math. Slovaca, Vol. 52, (2002), pp. 157–175.
• [3] A. Diego: “Sur les algébres de Hilbert”, Col. de Logique Math. Ser. A., Vol. 21, (1967), pp. 31–34.
• [4] W. Dudek: “On ideals in Hilbert algebras”, Acta Univ. Palack. Olom., Fac. rer. nat., Mathematica, Vol. 38, (1999), pp. 31–34.
• [5] R. Halaš: “Remarks on commutative Hilbert algebras”, Mathem. Bohemica, Vol. 127, (2002), pp. 525–529.

Identyfikatory

DOI

10.2478/s11533-007-0021-5