Idempotent semigroup. Call a semigroup idempotent if every element is idempotent.
0. Show that if a semigroup is idempotent and -trivial, then it is commutative.
1. Prove that if a semigroup is idempotent, then every -class is closed under multiplication (i.e. it is a sub-semigroup)
2. Prove that for every there are finitely many idempotent semigroups with generators.
Strongly connected automata. Let be a regular language with the following properties:
Prove that is trivial, i.e. empty or full.