Article in press
Authors:
Title:
Duality for Stonean Hilbert algebras
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2023-07-01 , Revised: 2024-04-09 , Accepted: 2024-04-11 , Available online: 2025-02-19 , https://doi.org/10.7151/dmgaa.1473
Abstract:
In this paper we characterize the dual space of Stonean Hilbeert algebras, a special kind of Hilbert algebras and we study the relationship between their structura and the monoid of their endomorphisms
Keywords:
Hilbert algebras, deductve system, Stone identity.
References:
- D. Bu\c{sneag}, On the maximal deductive systems of a bounded Hilbert algebra, Bull. Math. Soc. Math R.S. de Roumanie 31 (79) No. 1 (1987).
- D. Buşneag, Categories of Algebraic Logic, Ed. Academiei Române, 2006.
- S.A Celani, $\alpha$-ideals and $\alpha$-deductive systems in bounded Hilbert algebras, J.Mult.-Valued Logic & Soft Computing 21 (2013) 493–510.
- S.A. Celani and D. Montangie, Hilbert algebras with supremum, Algebra Univ. 67(3) (2012) 237–255.
https://doi.org/10.1007/s00012-012-0178-z - S.A. Celani, L.M. Cabrer and D. Montangie, Representation and duality for Hilbert algebras, Central Eur. J. Math. 7(3) (2009) 463–478.
https://doi.org/10.2478/s11533-009-0032-5 - S.A. Celani, A note on homomorphisms of Hilbert algebras, Int. J. Math. and Math. Sci. 29(1) (2002) 55–61.
https://doi.org/10.1155/S0161171202011134 - S.A. Celani, Notes on bounded Hilbert with supremum, Acta Sci. Math. 80 (2014) 3–19.
- A. Diego, Sur les algebres de Hilbert, Collection de Logique Mathematique, Ser. A (Ed. Hermann, Paris) 21 (1966) 1–52.
- I. Chajda, R. Halas and J. Kuhr, Semilattice Structures, Research and Exposition in Mathematics 30 (Heldermann Verlag, 2007).
- Ch.T. Dan, Hilbert Algebras of Fractions, Int. J. Math. and Math. Sci. Volume 2009.
https://doi.org/10.1155/2009/589830 - A. Figallo, E. Pick, S. Saad and M. Figallo, Free algebras in varieties of Hilbert algebras with supremum generated by finite chains, arXiv:1307.8184v1 [math.LO] 2013.
- H. Gaitán, Congruences and closure endomorphisms of Hilbert algebras, Commun. Algebra 43 (2015) 1135–1145.
https://doi.org/10.1080/00927872.2013.865039 - H. Gaitán, Duality for Hilbert algebras with supremum: an application, Math. Bohem. 142(3) (2017) 263–276.
https://doi.org/10.21136/MB.2017.0056-15 - H. Gaitán, Hilbert algebras with supremum generated by finite chains, Math. Slovaca 69(4) (2019) 953–963.
https://doi.org/10.1515/ms-2017-0262 - F. Guzman and C. Lynch, Varieties of positive implicative BCK-algebras subdirectly irreducible and free algebras, Math. Japonica 37 (1992) 27–39.
- P.M. Idziak, Lattice operations in BCK-algebras, Math. Japonica 29(6) (1984) 839–846.
- P.M. Idziak, Filters and congruences relations in BCK-algebras, Math. Japonica 29(6) (1984) 975–980.
- M. Kondo, Hilbert algebras are dual isomorphic to positive implicative BCK-algebras, Math. Japonica 49(2) (1999) 265–268.
- V. Koubek and H. Radovanská, Algebras determined by their endomorphism monoids, Cahiers de Topologie et Géometrie Deffréntielle Catégoriques 35(3) (1994) 187–225.
- A.S. Nasab and A.B. Saeid, Stonean Hilbert algebra, J. Intelligent & Fuzzy Systems 30 (2016) 485–492.
https://doi.org/10.3233/ifs-151773 - A.S. Nasab and A.B. Saeid, Some results in local Hilbert algebras, Math. Slovaca 67 (2017) 541–552.
https://doi.org/10.1515/ms-2016-0288 - R. Rasiowa, An Algebraic Approach to Non-classical Logics, Studies in Logic and the Foundations of Mathematics 8 (North Holland, Amsterdam Elsevier, New York, 1974).
Close