gK-algebra associated to polygroups

In this paper, we first introduce a generalized K-algebra (briefly, gK-algebra) $$(P, \cdot , \odot , e, ^{-1})$$ which is constructed on a non-symmetric polygroup $$(P, \cdot , e, ^{-1})$$ , by adjoining binary hyperoperation $$\odot $$ defined by $$x \odot y = x \cdot y^{-1}$$ , for all $$x, y \in P$$ . Then, we show that every gK-algebra associated to a canonical hypergroup is a hyper B-algebra with constant e. Finally, we define generalized gK-subalgebras, (prime) generalized gK-ideals, homomorphisms of $$(P, \cdot , \odot , e, ^{-1})$$ and quotient generalized gK-algebras.