Minimal algebra

Minimal algebra is an important concept in tame congruence theory, a theory that has been developed by Ralph McKenzie and David Hobby.
Definition.
A minimal algebra is a finite algebra with more than one element, in which every non-constant unary polynomial is a permutation on its domain.
Classification.
A polynomial of an algebra is a composition of its basic operations, formula_1-ary operations and the projections. Two algebras are called polynomially equivalent if they have the same universe and precisely the same polynomial operations. A minimal algebra formula_2 falls into one of the following types (P. P. Pálfy) 