Relatively inherently nonfinitely q-based semigroups
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- by Marcel Jackson and Mikhail Volkov PDF
- Trans. Amer. Math. Soc. 361 (2009), 2181-2206 Request permission
Abstract:
We prove that every semigroup $\mathbf {S}$ whose quasivariety contains a 3-nilpotent semigroup or a semigroup of index more than 2 has no finite basis for its quasi-identities provided that one of the following properties holds:
$\mathbf {S}$ is finite;
$\mathbf {S}$ has a faithful representation by injective partial maps on a set;
$\mathbf {S}$ has a faithful representation by order preserving maps on a chain.
As a corollary it is shown that, in an asymptotic sense, almost all finite semigroups and finite monoids admit no finite basis for their quasi-identities.
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Additional Information
- Marcel Jackson
- Affiliation: Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia
- Email: M.G.Jackson@latrobe.edu.au
- Mikhail Volkov
- Affiliation: Department of Mathematics, Ural State University, Ekaterinburg 620083, Russia
- Email: Mikhail.Volkov@usu.ru
- Received by editor(s): June 4, 2007
- Published electronically: November 25, 2008
- Additional Notes: The first author was supported by ARC Discovery Project Grant DP0342459
The second author acknowledges support from the Russian Foundation for Basic Research, grants 05-01-00540 and 06-01-00613. The paper was initiated during the second author’s Distinguished Fellowship at the Institute for Advanced Study of La Trobe University. - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 2181-2206
- MSC (2000): Primary 08C15, 20M20
- DOI: https://doi.org/10.1090/S0002-9947-08-04798-3
- MathSciNet review: 2465833