Duality for Hilbert algebras with supremum: An application

Hernando Gaitan

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 3, page 263-276
  • ISSN: 0862-7959

Abstract

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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 ∨ -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.

How to cite

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Gaitan, Hernando. "Duality for Hilbert algebras with supremum: An application." Mathematica Bohemica 142.3 (2017): 263-276. <http://eudml.org/doc/294143>.

@article{Gaitan2017,
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.},
author = {Gaitan, Hernando},
journal = {Mathematica Bohemica},
keywords = {Hilbert algebra; duality; monoid of endomorphisms; BCK-algebra},
language = {eng},
number = {3},
pages = {263-276},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Duality for Hilbert algebras with supremum: An application},
url = {http://eudml.org/doc/294143},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Gaitan, Hernando
TI - Duality for Hilbert algebras with supremum: An application
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 3
SP - 263
EP - 276
AB - 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.
LA - eng
KW - Hilbert algebra; duality; monoid of endomorphisms; BCK-algebra
UR - http://eudml.org/doc/294143
ER -

References

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  7. Gaitán, H., 10.1080/00927872.2013.865039, Commun. Algebra 43 (2015), 1135-1145. (2015) Zbl1320.03090MR3298124DOI10.1080/00927872.2013.865039
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