| It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. |
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| The elements of the semigroup are identified with the reduced words of the rewriting system. |
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| We show that the two définitions are really différent, even under strong restrictive conditions about the algebraic structure of the semigroup. |
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| It is known that the profinite completions of a free semigroup which are associated with a pseudovariety of semigroups or of ordered semigroups, can be defined by an écart or a quasi-écart. |
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| We also give some efficient algorithms to compute the Green relations, the local subsemigroups and the syntactic quasi-order of a subset of the semigroup. |
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| It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups. |
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| If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup. |
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| While this description of piecewise syndeticity looks somewhat forbidding, it has the advantage of making sense in any semigroup. |
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| In the case where the semigroup variety has a particular closure property with respect to programs, we are able to give precise characterizations of these regular languages. |
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| Equivalently a regular semigroup in which idempotents commute. |
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| Let S be a regular semigroup with set E of idempotent elements. |
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| In this paper we are going to follow their footsteps constructing the skew semigroup ring and prove its associativity without using approximate identity. |
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