TL;DR: In this paper, the notion of BG-algebras was introduced, which is a generalization of.B-algeses, and a non-empty set can be constructed from a nonempty set which is non-group derived.
Abstract: In this paper we introduce the notion of BG-algebras which is a generalization of .B-algebras. We construct a BG-algebra from a non-empty set, which is non-group-derived. Moreover, using the notion of normal subalgebra, we obtain several isomorphism theorems of BG-algebra and related properties.