Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 195-206 (2015)

On modal BE-algebras

O. Yousefi Kia, A. Rezaei and A. Borumand Saeid

Shahid Bahonar University of Kerman and Payame Noor University

Abstract: In this paper, we introduce modal BE-algebra and study some structural properties of modal BE-algebra. The notions of modal upper set, modal BE-filter, BE-tautology filter, dual modal BE-algebra and quotient modal BE-algebraare introduced and their basic properties are investigated. We will prove that every self- distributive BE-algebra, induce a dual modal BE-algebra. Finally, we will prove that every dual modal BE-algebra is a modal BE-algebras under special conditions.

Keywords: Self distributive, commutative, bounded, involutory, modal BE-algebra, modal (normal) BE-filter.

Classification (MSC2000): 06F35; 03G25

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