A Counterexample in Galois Theory
Thomas W. Hungerford · American Mathematical Monthly · 1990
in the theorem is J = (b) = {b, ab, ba, aba,O}. The machine M1 in FIGURE 6 has semigroup S(M1) = (1, a,O} Z2 U {O} which is a group with zero, the machine M2 has semigroup S(M2) = Jl (the semigroup J with identity adjoined) where J contains no units, and M1 ED M2 covers M. Note that the semigroups of M1 and M2 are simpler than the semigroup of M, even though the diagrams are a bit more complicated.