Mathematica Bohemica, Vol. 142, No. 3, pp. 263-276, 2017
Duality for Hilbert algebras with supremum: An application
Received September 24, 2015. First published January 2, 2017.
Abstract: We modify slightly the definition of $H$-partial functions given by Celani and Montangie (2012); these partial functions are the morphisms in the category of $H^\vee$-space and this category is the dual category of the category with objects the Hilbert algebras with supremum and morphisms, the algebraic homomorphisms. As an application we show that finite pure Hilbert algebras with supremum are determined by the monoid of their endomorphisms.
Keywords: Hilbert algebra; duality; monoid of endomorphisms; BCK-algebra
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Affiliations: Hernando Gaitán, Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional de Colombia, Ciudad Universitaria, Bogotá, Colombia, e-mail: email@example.com