Abstract
In this paper, we introduce the notion of Σ-hyperalgebras for an arbitrary signature Σ and provide some examples. Then we extend the
notions of several kinds of homomorphisms and study their properties.
Also, we study subhyperalgebras of a Σ-hyperalgebra A, Sub(A), under
algebraic closure operators S, H and I. Finally, we introduce the notions
of closed, invertible, ultraclosed and conjugable subhyperalgebras and
investigate their connections to each other.