Abstract
The concept of gamma((alpha,beta))-BE-algebra is introduced as a generalization of a gamma(alpha)-BE-algebra and a gamma(beta)-BE-algebra and its properties are studied. We introduced the concepts of (alpha, beta)-subalgebra and (alpha, beta)-filter of a gamma((alpha,beta))-BE-algebra and discussed the relation between these two concepts. We provided conditions for an (alpha, beta)-subalgebra to be an (alpha, beta)-filter. We provided equivalent conditions for the formation of an (alpha, beta)-filter from a nonempty subset of a gamma((alpha,beta))-BE-algebra. We introduced the concept of (alpha, beta)-atomic gamma((alpha,beta))-BE-algebra and studied its properties. We introduced the concept of atomic (alpha, beta)-filter a gamma((alpha,beta))-BE-algebra and gave the necessary and sufficient condition for an (alpha, beta)-filter to be atomic.