Some properties of epimorphisms of Hilbert algebras

• Autorzy: Dumitru Buşneag , Mircea Ghiţă
• Języki publikacji: EN

Abstrakty

EN

This paper represents a start in the study of epimorphisms in some categories of Hilbert algebras. Even if we give a complete characterization for such epimorphisms only for implication algebras, the following results will make possible the construction of some examples of epimorphisms which are not surjective functions. Also, we will show that the study of epimorphisms of Hilbert algebras is equivalent with the study of epimorphisms of Hertz algebras.

Słowa kluczowe

EN

Hilbert algebras; Hertz algebras; Implication algebras; Tarski algebras; Boole algebras; Deductive systems; Epimorphisms

Kategorie tematyczne

• 18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
• 03G25: Other algebras related to logic
• 18C05: Equational categories

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 41-52

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Dumitru Buşneag

• University of Craiova

autor

Mircea Ghiţă

• University of Craiova

Bibliografia

• [1] Balbes R., Dwinger Ph., Distributive lattices, Missouri Univ. Press, Columbia, Missouri, 1975
• [2] Buşneag D., Categories of algebraic logic, Editura Academiei Române, Bucharest, 2006
• [3] Celani S.A., Cabrer L.M., Duality for finite Hilbert algebras, Discrete Math., 2005, 305(1–3), 74–99 http://dx.doi.org/10.1016/j.disc.2005.09.002
• [4] Celani S.A., Cabrer L.M., Topological duality for Tarski algebras, Algebra Universalis, 2007, 58, 73–94 http://dx.doi.org/10.1007/s00012-007-2041-1
• [5] Diego A., Sur les algèbres de Hilbert, Collection de Logique Mathematique, Série A, 1966, 21, 1–54 (in French)
• [6] Figallo Jr A., Ziliani A., Remarks on Hertz algebras and implicative semilattices, Bull. Sect. Logic Univ. Lódz, 2005, 1(34), 37–42
• [7] Figallo A.V., Ramon G., Saad S., A note on the Hilbert algebras with infimum, Math. Contemp., 2003, 24, 23–37
• [8] Gluschankof D., Tilli M., Maximal Deductive Systems and Injective Objects in the Category of Hilbert Algebras, Zeitschr. Für Math. Logik und Grundlagen der Math., 1988, 34, 213–220 http://dx.doi.org/10.1002/malq.19880340305
• [9] Jun Y.B., Commutative Hilbert Algebras, Soochow J. Math., 1996, 22(4), 477–484
• [10] Porta H., Sur quelques algèbres de la Logique, Port. Math., 1981, 40(1), 41–77
• [11] Rasiowa H., An algebraic approach to non-classical logics, Stud. Logic Found. Math., 1974, 78
• [12] Torrens A., On The Role of The Polynomial (X → Y) → Y in Some Implicative Algebras, Zeitschr. Für Math. Logik und Grundlagen der Math., 1988, 34(2), 117–122 http://dx.doi.org/10.1002/malq.19880340205
• [13] Taşcău D.D., Some properties of the operation x ∪ y = (x → y) → ((y → x) → x) in a Hilbert algebra, An. Univ. Craiova Ser. Mat. Inform., 2007, 34(1), 78–81

Identyfikatory

DOI

10.2478/s11533-009-0070-z