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ISSN 1088-6850(e) ISSN 0002-9947(p)

Relatively inherently nonfinitely q-based semigroups

Author(s): Marcel Jackson; Mikhail Volkov
Journal: Trans. Amer. Math. Soc. 361 (2009), 2181-2206.
MSC (2000): Primary 08C15, 20M20
Posted: November 25, 2008
MathSciNet review: 2465833
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Abstract: We prove that every semigroup ${\bf S}$ 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:

${\bf S}$ is finite;
${\bf S}$ has a faithful representation by injective partial maps on a set;
${\bf S}$ 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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