Monadic BE-algebras

Article type: Research Article

Authors: Zaheriani, Seyed Yashar | Zahiri, Omid

Affiliations: Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran

Note: [] Corresponding author. Omid Zahiri, Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran. E-mail: om.zahiri@gmail.com

Abstract: The aim of this paper is to introduce and investigate (bounded commutative) monadic BE-algebras. It's proved that for each m-relatively complete subalgebra of a bounded commutative monadic BE-algebra, we can defined a bounded commutative monadic BE-algebra, moreover, each bounded commutative monadic BE-algebra is of this form. Also, some results about filters and congruences on a bounded commutative monadic BE-algebra are stated and a relation between bounded commutative monadic BE-algebras and monadic bounded residuated lattices is obtained.

Keywords: Monadic, BE-algebra, relatively complete subalgebra, congruence, m-filter

DOI: 10.3233/IFS-141257

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 6, pp. 2987-2995, 2014