Relation Between Be-Algebras and G-Hilbert Algebras
Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was d...
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doaj-32d07c801539476f94b4511d4cc8ba652021-09-05T17:19:43ZengSciendoDiscussiones Mathematicae - General Algebra and Applications2084-03732018-06-01381334610.7151/dmgaa.1285dmgaa.1285Relation Between Be-Algebras and G-Hilbert AlgebrasRezaei Akbar0Saeid Arsham Borumand1Department of Mathematics Payame Noor University P.O. Box 19395-3697, Tehran, IranDepartment of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Kerman, IranHilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was defined the notion of g-Hilbert algebra. In this paper, we investigate the relationship between g-Hilbert algebras, gi-algebras, implication gruopoid and BE-algebras. In fact, we show that every g-Hilbert algebra is a self distributive BE-algebras and conversely. We show cannot remove the condition self distributivity. Therefore we show that any self distributive commutative BE-algebras is a gi-algebra and any gi-algebra is strong and transitive if and only if it is a commutative BE-algebra. We prove that the MV -algebra is equivalent to the bounded commutative BE-algebra.https://doi.org/10.7151/dmgaa.1285(heytingimplication(g-)hilbert) algebrabe/ci-algebradual (s/q/bck)-algebragi-algebraimplication groupoidpre-logicmv - algebra06d2006f3503g25 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rezaei Akbar Saeid Arsham Borumand |
spellingShingle |
Rezaei Akbar Saeid Arsham Borumand Relation Between Be-Algebras and G-Hilbert Algebras Discussiones Mathematicae - General Algebra and Applications (heyting implication (g-)hilbert) algebra be/ci-algebra dual (s/q/bck)-algebra gi-algebra implication groupoid pre-logic mv - algebra 06d20 06f35 03g25 |
author_facet |
Rezaei Akbar Saeid Arsham Borumand |
author_sort |
Rezaei Akbar |
title |
Relation Between Be-Algebras and G-Hilbert Algebras |
title_short |
Relation Between Be-Algebras and G-Hilbert Algebras |
title_full |
Relation Between Be-Algebras and G-Hilbert Algebras |
title_fullStr |
Relation Between Be-Algebras and G-Hilbert Algebras |
title_full_unstemmed |
Relation Between Be-Algebras and G-Hilbert Algebras |
title_sort |
relation between be-algebras and g-hilbert algebras |
publisher |
Sciendo |
series |
Discussiones Mathematicae - General Algebra and Applications |
issn |
2084-0373 |
publishDate |
2018-06-01 |
description |
Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was defined the notion of g-Hilbert algebra. In this paper, we investigate the relationship between g-Hilbert algebras, gi-algebras, implication gruopoid and BE-algebras. In fact, we show that every g-Hilbert algebra is a self distributive BE-algebras and conversely. We show cannot remove the condition self distributivity. Therefore we show that any self distributive commutative BE-algebras is a gi-algebra and any gi-algebra is strong and transitive if and only if it is a commutative BE-algebra. We prove that the MV -algebra is equivalent to the bounded commutative BE-algebra. |
topic |
(heyting implication (g-)hilbert) algebra be/ci-algebra dual (s/q/bck)-algebra gi-algebra implication groupoid pre-logic mv - algebra 06d20 06f35 03g25 |
url |
https://doi.org/10.7151/dmgaa.1285 |
work_keys_str_mv |
AT rezaeiakbar relationbetweenbealgebrasandghilbertalgebras AT saeidarshamborumand relationbetweenbealgebrasandghilbertalgebras |
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1717786565979144192 |