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Quasi-identities of finite semigroups and symbolic dynamics

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Abstract

An algebra is inherently non-finitely (Q-)based if it is not a member of any locally finite (quasi-)variety, whose (quasi-)identities are finitely based. We prove that no finite semigroup is inherently non-finitely Q-based. This is in marked contrast to the case of varieties, where there are many inherently non-finitely based finite semigroups which have all been described by the second author.

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Authors and Affiliations

  1. Department of Computer Science and Engineering Center for Communication and Information Sciences, University of Nebraska-Lincoln, 68588, Lincoln, NE, USA

    Stuart W. Margolis & Mark V. Sapir

  2. Department of Mathematics and Statistics Center for Communication and Information Sciences, University of Nebraska-Lincoln, 68588, Lincoln, NE, USA

    Stuart W. Margolis & Mark V. Sapir

Authors
  1. Stuart W. Margolis
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  2. Mark V. Sapir
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Correspondence to Stuart W. Margolis.

Additional information

Research of both authors supported in part by NSF and the Center for Communication and Information Sciences of the University of Nebraska at Lincoln.

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Margolis, S.W., Sapir, M.V. Quasi-identities of finite semigroups and symbolic dynamics. Israel J. Math. 92, 317–331 (1995). https://doi.org/10.1007/BF02762086

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  • DOI: https://doi.org/10.1007/BF02762086

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