Abstract
LetA=(M, S, δ) be an automaton without outputs whereM is a nonemptyset andS is a nonempty semigroup. Then the right congruences μM and μ m associated withS have been expressed in many different ways (μ M is called the Myhill-Nerode congruence onS). Also, their algebraic properties have been investigated. We have introduced the right congruences μ S and μα onM and we have obtained necessary and sufficient conditions thatS/μ andM/w have nontrivialS-homomorphisms where μ andw are any right congruences onS andM respectively. The faithfulness ofS has been introduced.
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