Finite Aperiodic Semigroups with Commuting Idempotents and Generalizations
نویسندگان
چکیده
Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their corresponding syntactic semigroups. The Eilenberg Variety Theorem [E] establishes a one-one correspondence between so called varieties of formal languages and pseudovarieties of finite semigroups. Recall that a pseudovariety is a collection of finite semigroups closed under homomorphic image, subsemigroups and (finite) direct product. The books by Eilenberg [E], Lallement [L], Pin [P] and Almeida [Al] give many details about this field.
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