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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:
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
Descripción
Sumario: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].