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An infinite order operator on the lattice of varieties of completely regular semigroups

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Abstract

Let\(U\) be a variety of completely regular semigroups. Define\(U\) C * to be the class of all completely regular semigroupsS whose least full and self-conjugate subsemigroupC *(S) belongs to\(U\). ThenC * is an operator on the lattice\(L(CR)\) of varieties of completely regular semigroups. In this note we show that the order ofC * is infinite. This fact yields that the Mal'cev project is not associative on\(L(CS)\). We describe\(U\)(C *)1,\(U\) ∈\([RB,CS]\) andi ≥ 0, in terms of ℰ-invariant normal subgroups of the free group over a countably infinite set. The lattice theoretic properties ofC * are also studied.

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  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    S. Zhang

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  1. S. Zhang
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Zhang, S. An infinite order operator on the lattice of varieties of completely regular semigroups. Algebra Universalis 35, 485–505 (1996). https://doi.org/10.1007/BF01243591

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  • DOI: https://doi.org/10.1007/BF01243591

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