# Representation of Hilbert algebras and implicative semilattices

Open Mathematics (2003)

- Volume: 1, Issue: 4, page 561-572
- ISSN: 2391-5455

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topSergio Celani. "Representation of Hilbert algebras and implicative semilattices." Open Mathematics 1.4 (2003): 561-572. <http://eudml.org/doc/268848>.

@article{SergioCelani2003,

abstract = {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.},

author = {Sergio Celani},

journal = {Open Mathematics},

keywords = {03G25; 06A12; 06E15},

language = {eng},

number = {4},

pages = {561-572},

title = {Representation of Hilbert algebras and implicative semilattices},

url = {http://eudml.org/doc/268848},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Sergio Celani

TI - Representation of Hilbert algebras and implicative semilattices

JO - Open Mathematics

PY - 2003

VL - 1

IS - 4

SP - 561

EP - 572

AB - 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.

LA - eng

KW - 03G25; 06A12; 06E15

UR - http://eudml.org/doc/268848

ER -

## References

top- [1] D. Busneag: “A note on deductive systems of a Hilbert algebra”, Kobe Journal of Mathematics, Vol. 2, (1985), pp. 29–35. Zbl0584.06005
- [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 Zbl0993.03089
- [3] S.A. Celani: “Topological Representation of Distributive Semilattices”, Scientiae Mathematicae Japonicae online, Vol. 8, (2003), pp. 41–51. Zbl1041.06002
- [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. Zbl0657.03032
- [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. Zbl0920.06011
- [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 Zbl0473.06003
- [9] W.C. Nemitz: “Implicative semi-lattices”, Trans. Amer. Math. Soc., Vol. 117, (1965), pp. 128–142. http://dx.doi.org/10.2307/1994200 Zbl0128.24804

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