Some Unitary Operators on Hoop-algebras

In this paper, we introduce the notions of multiplier, $\odot$-closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, $\odot$-closure operator and modal operator on hoop-algebras. Then we study relationships between multiplier and closure operator on hoop-algebras showing that, any monotone modal operator on hoop-algebra serves as a closure operator. Finally we represent image of hoop-algebra under the closure operator can be a hoop-algebra.