Γ-BE-algebras

Abstract

We introduce the concept of Γ-BE-algebra as a generalization of a BE-algebra and study its properties. For a fixed binary operation α in a set Γ of binary operations on a non-empty set X, we introduce the concepts of β-reflexive, βtransitive, β-antisymmetric, α-transitive, α-left distributive and γ-left distributive Γα-BE-algebra and study the relations between them. We introduce the concept of β-subalgebra and β-filter in a Γα-BE-algebra and study the relation between α-subalgebra, α-filter and β-subalgebra in a Γα-BE-algebra.

Key words and phrases. BE-algebra, Γ-BE-algebra, Γα-BE-algebra, subalgebra, filter.

2010 Mathematics Subject Classification. 03G25, 06F35.