A new generalization of BE-algebras

In this paper we introduce the notion of [Formula: see text]-algebras as a generalization of BE-algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in [Formula: see text]-algebras. More...

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Detalles Bibliográficos
Autores principales: Yiarayong, Pairote, Wachirawongsakorn, Piyada
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6197410/
https://www.ncbi.nlm.nih.gov/pubmed/30364568
http://dx.doi.org/10.1016/j.heliyon.2018.e00863
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author Yiarayong, Pairote
Wachirawongsakorn, Piyada
author_facet Yiarayong, Pairote
Wachirawongsakorn, Piyada
author_sort Yiarayong, Pairote
collection PubMed
description In this paper we introduce the notion of [Formula: see text]-algebras as a generalization of BE-algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in [Formula: see text]-algebras. Moreover, we investigate relationships between left ideals and filters in [Formula: see text]-algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if I be a left ideal of a [Formula: see text]-algebra X, then [Formula: see text] is a left ideal of X for all [Formula: see text].
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spelling pubmed-61974102018-10-24 A new generalization of BE-algebras Yiarayong, Pairote Wachirawongsakorn, Piyada Heliyon Article In this paper we introduce the notion of [Formula: see text]-algebras as a generalization of BE-algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in [Formula: see text]-algebras. Moreover, we investigate relationships between left ideals and filters in [Formula: see text]-algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if I be a left ideal of a [Formula: see text]-algebra X, then [Formula: see text] is a left ideal of X for all [Formula: see text]. Elsevier 2018-10-17 /pmc/articles/PMC6197410/ /pubmed/30364568 http://dx.doi.org/10.1016/j.heliyon.2018.e00863 Text en © 2018 The Authors http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Article
Yiarayong, Pairote
Wachirawongsakorn, Piyada
A new generalization of BE-algebras
title A new generalization of BE-algebras
title_full A new generalization of BE-algebras
title_fullStr A new generalization of BE-algebras
title_full_unstemmed A new generalization of BE-algebras
title_short A new generalization of BE-algebras
title_sort new generalization of be-algebras
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6197410/
https://www.ncbi.nlm.nih.gov/pubmed/30364568
http://dx.doi.org/10.1016/j.heliyon.2018.e00863
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