Representation of Hilbert algebras and implicative semilattices

Sergio Celani

Open Mathematics (2003)

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

Abstract

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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.

How to cite

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Sergio 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

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  1. [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. [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. [3] S.A. Celani: “Topological Representation of Distributive Semilattices”, Scientiae Mathematicae Japonicae online, Vol. 8, (2003), pp. 41–51. Zbl1041.06002
  4. [4] A. Diego: “Sur les algébras de Hilbert”, Colléction de Logique Math., Serie A, No. 21, Gauthiers-Villars, Paris, (1966). 
  5. [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. [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. [7] A. Monteiro: “Sur les algèbras de Heyting symmétriques”, Portugaliae Mathematica, Vol. 39, (1980), pp. 1–239. 
  8. [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. [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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