Γα, β-BE-Algebras. (24th February 2023) - Bandaru, Ravikumar; Kang, Jeong Gi; Alali, Amal S.; Jun, Young Bae
Abstract : The concept of Γ α, β -BE-algebra is introduced as a generalization of a Γ α -BE-algebra and a Γ β -BE-algebra and its properties are studied. We introduced the concepts of α, β -subalgebra and α, β -filter of a Γ α, 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 Γ α, β -BE-algebra. We introduced the concept of α, β -atomic Γ α, β -BE-algebra and studied its properties. We introduced the concept of atomic α, β -filter a Γ α, β -BE-algebra and gave the necessary and sufficient condition for an α, β -filter to be atomic.