Study of Hilbert algebras in point of filters

Nasab, Ali Soleimani; Saeid, Arsham Borumand

doi:10.1515/auom-2016-0039

Abstract

The aim of this work is to introduce some types of filters in Hilbert algebras. Some theorems are stated and proved which determine the relationship between these notions and other filters of Hilbert algebra and by some examples we show that these concepts are different. The relationships between these filters and quotient algebras that are constructed via these filters are described.

References

[1] Buşneag D., Categories of algebraic logic, Ed. Academiei Rom^ane, 2006.
Search in Google Scholar Back to article
[2] Buşneag D., Contributions to the study of Hilbert algebras (in romanian), PhD Thesis, Univ. of Bucharest, 1985.
Search in Google Scholar Back to article
[3] Buşneag D., On the maximal deductive system of a bounded Hilbert algebra, Bull. Math. Soc. Sci. Math. Roumanie, Tome 31(79), nr. 1(1987), 9-21.
Search in Google Scholar Back to article
[4] Buşneag D., Ghita M., Some latticial properties of Hilbert algebras, Bull. Math. Soc. Sci. Math. Roumanie Tome 53(101) No. 2(2010), 87-107.
Search in Google Scholar Back to article
[5] Celani S. A., α-Ideal and α - Deductive Systems in Bounded Hilbert algebras, J. of Mult. valued Logic and Soft Computing, Vol. o, (2013), 1-18.
Search in Google Scholar Back to article
[6] Celani S. A., Jansana R., On the free implicative semilattice extension of a Hilbert algebra, Mathematical Logic Quarterly 58(3), (2012), 1-20.10.1002/malq.201020098
Search in Google Scholar Back to article
[7] Celani S. A., Montangie D., Hilbert algebras with supremum, Algebra Universalis, 67 (2012), 237-255.10.1007/s00012-012-0178-z
Search in Google Scholar Back to article
[8] Diego A., Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.
Search in Google Scholar Back to article
[9] Figallo A. V., Ram_on G. Z., Saad S., A note on the Hilbert algebras with in_mum, Math. Contemp. 24(2003), 23-37.
Search in Google Scholar Back to article
[10] Gluschankof D., Tilli M., Maximal deductive systems and injective objects in the category of Hilbert algebras, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 34, No.3 (1988), 213-220.10.1002/malq.19880340305
Search in Google Scholar Back to article
[11] Hong S. M., Jun Y. B., On deductive systems of Hilbert algebras, Comm. Korean Math. Soc. 11:3(1996), 595-600.
Search in Google Scholar Back to article
[12] Köhler P., Brouwerian semilattices. Trans. Amer. Math. Soc. Vol.268,(1981), 103-126.10.2307/1998339
Search in Google Scholar Back to article
[13] Monteiro A., Sur les alg_ebres de Heyting sym_etriques. Portugaliae Mathematica 39 (1980), fasc. 1-4.
Search in Google Scholar Back to article
[14] Nemitz W.C., Implicative semi-lattices. Trans. Amer. Math. Soc. 117,(1965), 128-142.10.1090/S0002-9947-1965-0176944-9
Search in Google Scholar Back to article
[15] Piciu D., Algebras of fuzzy logic, Ed. Universitaria, Craiova (2007).
Search in Google Scholar Back to article
[16] Porta H., Sur quelques alg_ebres de la Logique.Portugaliae Mathematica. Vol 40, Fasc 1(1981) 41-77.
Search in Google Scholar Back to article
[17] Van Gasse B., Deschrijver G., Cornelis C., Kerre E.E., Filters of residuated lattices and triangle algebra, Inf. Sci. 180(16) (2010) 3006-3020.10.1016/j.ins.2010.04.010
Search in Google Scholar Back to article

Study of Hilbert algebras in point of filters

Abstract

Paradigm

My account