Some Unitary Operators on Hoop-algebras

Abstract

In this paper, we introduce the notions of multiplier, ⊙-closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, ⊙-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.

Keywords

• Hoop-algebra
• Multiplier
• ⊙-closure operator
• Modal operator
• Homomorphism