Hilbert algebras with supremum generated by finite chains-Reference-Cited by-同舟云学术

Hilbert algebras with supremum generated by finite chains

Published:2019-07-19 Issue:4 Volume:69 Page:953-963
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Gaitán Hernando¹

Affiliation:

1. Departamento de Matemáticas Facultad de Ciencias , Universidad Nacional de Colombia Ciudad Universitaria , Bogotá , Colombia

Abstract

Abstract Based on the work of A. Monteiro, A. Torrens, and D. Buşneag, in this paper we point out that the dual space of Hilbert algebras with supremum generated by chains depends, modulo the dual space of a Hilbert algebra with supremum defined by S. Celani an D. Montangie, exclusively, on the order carried out by the topological space. We use such a characterization to prove that a bounded Hilbert algebra generated by chains is determined by the monoid of its endomorphisms.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0262/pdf

Reference13 articles.

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3. BuşNeag, D.—Ghită, M.: Some latticial properties of Hilbert algebras, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 53(101) (2010), 87-107.

4. Celani, S.—Cabrer, L.: Duality for finite Hilbert algebras, Discrete Mathematics 305 (2005), 74–99.

5. Celani, S. A.—Cabrer, L. M.—Montangie, D.: Representation and duality for Hilbert algebras, Cent. Eur. J. Math. 7(3) (2009), 463–478.