| Summary: | The concept of Γα,β-BE-algebra is introduced as a generalization of a Γα-BE-algebra and a Γβ-BE-algebra and its properties are studied. We introduced the concepts of α,β-subalgebra and α,β-filter of a Γα,β-BE-algebra and discussed the relation between these two concepts. We provided conditions for an α,β-subalgebra to be an α,β-filter. We provided equivalent conditions for the formation of an α,β-filter from a nonempty subset of a Γα,β-BE-algebra. We introduced the concept of α,β-atomic Γα,β-BE-algebra and studied its properties. We introduced the concept of atomic α,β-filter a Γα,β-BE-algebra and gave the necessary and sufficient condition for an α,β-filter to be atomic.
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