A new generalization of BE-algebras

In this paper we introduce the notion of PSRU-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 PSRU-algebras. Moreover, we investigate relations...

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Bibliographic Details
Published in:Heliyon 2018-10, Vol.4 (10), p.e00863-e00863, Article e00863
Main Authors: Yiarayong, Pairote, Wachirawongsakorn, Piyada
Format: Article
Language:English
Subjects:
Mathematics
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Summary:In this paper we introduce the notion of PSRU-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 PSRU-algebras. Moreover, we investigate relationships between left ideals and filters in PSRU-algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if I be a left ideal of a PSRU-algebra X, then Ix is a left ideal of X for all x∈X.
ISSN:2405-8440
2405-8440
DOI:10.1016/j.heliyon.2018.e00863