Abstract
In this paper, we introduce and study states on hyper MV-algebras. First, we introduce the notions of Riečan states and Bosbach states on a hyper MV-algebra and derive some properties of them. Also, we investigate and characterize regular Riečan states and regular Bosbach states on a hyper MV-algebra. Moreover, using a Bosbach state on a hyper MV-algebra, we construct and discuss a quotient hyper MV-algebra. In particular, we obtain some equivalent conditions under which a quotient hyper MV-algebra becomes a Boolean algebra. Finally, we introduce the notion of state morphisms on hyper MV-algebras, and discuss some relationships between state morphisms and Bosbach states.
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