Some properties of epimorphisms of Hilbert algebras

Dumitru Buşneag; Mircea Ghiţă

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 41-52
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dumitru Buşneag, and Mircea Ghiţă. "Some properties of epimorphisms of Hilbert algebras." Open Mathematics 8.1 (2010): 41-52. <http://eudml.org/doc/269087>.

@article{DumitruBuşneag2010,
abstract = {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.},
author = {Dumitru Buşneag, Mircea Ghiţă},
journal = {Open Mathematics},
keywords = {Hilbert algebras; Hertz algebras; Implication algebras; Tarski algebras; Boole algebras; Deductive systems; Epimorphisms; implication algebras; Boolean algebras; deductive systems; epimorphisms; categories of algebraic logic},
language = {eng},
number = {1},
pages = {41-52},
title = {Some properties of epimorphisms of Hilbert algebras},
url = {http://eudml.org/doc/269087},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Dumitru Buşneag
AU - Mircea Ghiţă
TI - Some properties of epimorphisms of Hilbert algebras
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 41
EP - 52
AB - 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.
LA - eng
KW - Hilbert algebras; Hertz algebras; Implication algebras; Tarski algebras; Boole algebras; Deductive systems; Epimorphisms; implication algebras; Boolean algebras; deductive systems; epimorphisms; categories of algebraic logic
UR - http://eudml.org/doc/269087
ER -

References

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  1. [1] Balbes R., Dwinger Ph., Distributive lattices, Missouri Univ. Press, Columbia, Missouri, 1975 Zbl0231.06017
  2. [2] Buşneag D., Categories of algebraic logic, Editura Academiei Române, Bucharest, 2006 Zbl05191994
  3. [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 Zbl1084.03050
  4. [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. [5] Diego A., Sur les algèbres de Hilbert, Collection de Logique Mathematique, Série A, 1966, 21, 1–54 (in French) 
  6. [6] Figallo Jr A., Ziliani A., Remarks on Hertz algebras and implicative semilattices, Bull. Sect. Logic Univ. Lódz, 2005, 1(34), 37–42 Zbl1114.03312
  7. [7] Figallo A.V., Ramon G., Saad S., A note on the Hilbert algebras with infimum, Math. Contemp., 2003, 24, 23–37 Zbl1082.03057
  8. [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 Zbl0657.03032
  9. [9] Jun Y.B., Commutative Hilbert Algebras, Soochow J. Math., 1996, 22(4), 477–484 Zbl0864.03042
  10. [10] Porta H., Sur quelques algèbres de la Logique, Port. Math., 1981, 40(1), 41–77 
  11. [11] Rasiowa H., An algebraic approach to non-classical logics, Stud. Logic Found. Math., 1974, 78 
  12. [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 Zbl0621.03043
  13. [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 Zbl1174.03358

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