Representation of Hilbert algebras and implicative semilattices

• Autorzy: Sergio Celani
• Języki publikacji: EN

Abstrakty

EN

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.

Słowa kluczowe

EN

Hilbert algebras; implicative semilattices; topological representation; duality; Boolean ring; 03G25; 06A12; 06E15

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 4
• Strony: 561-572

Daty

wydano

2003-12-01

online

2003-12-01

Twórcy

autor

Sergio Celani

• Universidad Nacional del Centro and CONICET

Bibliografia

• [1] D. Busneag: “A note on deductive systems of a Hilbert algebra”, Kobe Journal of Mathematics, Vol. 2, (1985), pp. 29–35.
• [2] S.A. Celani: “A note on Homomorphisms of Hilbert Algebras”, International Journal of Mathematical and Mathematics Science, Vol. 29, (2002), pp. 55–61. http://dx.doi.org/10.1155/S0161171202011134
• [3] S.A. Celani: “Topological Representation of Distributive Semilattices”, Scientiae Mathematicae Japonicae online, Vol. 8, (2003), pp. 41–51.
• [4] A. Diego: “Sur les algébras de Hilbert”, Colléction de Logique Math., Serie A, No. 21, Gauthiers-Villars, Paris, (1966).
• [5] D. Gluschankof and M. Tilli: “Maximal deductive systems and injective objects in the category of Hilbert algebras”, Zeitschr. f. math. Logik und Grundlagen. d. math., Vol. 34, (1988), pp. 213–220.
• [6] J. Meng, Y.B. Jun, S.M. Hong: “Implicative semilattices are equivalent to positive implicative BCK-algebras with condition (S)”, Math. Japonica, Vol. 48, (1998), pp. 251–255.
• [7] A. Monteiro: “Sur les algèbras de Heyting symmétriques”, Portugaliae Mathematica, Vol. 39, (1980), pp. 1–239.
• [8] P. Köhler: “Brouwerian semilattices”, Trans. Amer. Math. Soc., Vol. 268, (1981), pp. 103–126. http://dx.doi.org/10.2307/1998339
• [9] W.C. Nemitz: “Implicative semi-lattices”, Trans. Amer. Math. Soc., Vol. 117, (1965), pp. 128–142. http://dx.doi.org/10.2307/1994200

Identyfikatory

DOI

10.2478/BF02475182