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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The syntactic monoid of an infix code

Authors: Mario Petrich and Gabriel Thierrin
Journal: Proc. Amer. Math. Soc. 109 (1990), 865-873
MSC: Primary 68Q45
MathSciNet review: 1010804
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Abstract: Necessary and sufficient conditions on a monoid $ M$ are found in order that $ M$ be isomorphic to the syntactic monoid of a language $ L$ over an alphabet $ X$ having one of the following properties. In the first theorem $ L$ is a $ {P_L}$-class and $ {P_{W\left( L \right)}} \subseteq {P_L}$ where $ {P_L}$ is the syntactic congruence of $ L$ and $ W\left( L \right)$ is the residue of $ L$. In the second theorem $ L$ is an infix code; that is, satisfies $ u,uvw \in L$ implying $ u = w = 1$. In the third theorem $ L$ is an infix code satisfying a condition which amounts to the requirement that $ M$ be a nilmonoid. Various refinements of these conditions are also considered.

References [Enhancements On Off] (What's this?)

  • [1] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. II, Amer. Math. Soc., Providence, RI, 1967. MR 0218472 (36:1558)
  • [2] H. Jürgensen and G Thierrin, Infix codes, Proc. Fourth Hungarian Comp. Sci. Conf., Györ (1985), 25-29. MR 844331 (87f:68045)
  • [3] B. M. Schein, Homomorphisms of subdirect decompositions of semigroups, Pacific J. Math. 17 (1966), 529-547. MR 0197603 (33:5768)
  • [4] G. Thierrin, The syntactic monoid of a hypercode, Semigroup Forum 6 (1973), 227-231. MR 0376935 (51:13110)
  • [5] -, Sur la structure des demi-groupes, Alger Math. 3 (1956), 161-171. MR 0100642 (20:7071)

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Keywords: Monoid, language, congruence, syntactic, code, infix
Article copyright: © Copyright 1990 American Mathematical Society

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