γ-hyperalgebras, regular and strongly regular relations on them

Abstract

In this paper, we generalize the notion of algebra and Γ-algebra over a field. A Γ-hyperalgebra is an algebraic structure consisting of a hypervector space V over a Krasner hyperfield K, a hypergroupoid Γ together with a mapping from V × Γ × V to P^∗(V). We study regular relations on Γ-hyperalgebras. Also, we introduce an equivalence relation γ^∗ on a T-hyperalgebra V and we show that it is strongly regular relation. Furthermore, V/γ^∗, the set of all equivalence classes of this equivalence relation, is a Γ/β^∗-algebra over the field K/α^∗. Finally, we show that there is a covariant functor between the category of Γ-hyperalgebras and the category of algebras.