Convex automorphisms of partial monounary algebras
A representation of cyclically ordered sets by means of partial semigroups with an additional unary operation is constructed.
It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
In this paper the notion of an interval in a partial monounary algebra is introduced and pairs , of partial monounary algebras are investigated such that each interval in is also an interval in , and conversely.