Unary Minimal Partial Hyperclones

Jovanka Pantovic, Biljana Rodic and Gradimir Vojvodic

In this paper, we study unary minimal partial hyperclones. Every unary minimal partial hyperclone is minimal hyperclone or minimal proper partial clone. Since all minimal proper partial clones are already known, it left to characterize all minimal hyperclones. There is a full order embedding of the lattice of hyperclones on A generated by unary hyperoperations into the lattice of clones on P (A) \{Ø}, that we use to give characterisation of unary minimal partial hyperclones. As examples, we determine all unary minimal hyperclones on two and three element sets.