Abstract
Completely regular semigroups with the unary operation of inversion within their maximal subgroups form a variety under inclusion denoted by \(\mathcal {C}\mathcal {R}\). The lattice of its subvarieties is denoted by \(\mathcal {L}(\mathcal {C}\mathcal {R})\). Kernel, trace, left trace and right trace relations on \(\mathcal {L}(\mathcal {C}\mathcal {R})\) induce operators which can be used to produce networks. For the pairs (kernel, trace)- and (left trace, right trace)-networks we establish strong properties. We consider examples of local- and core-relations networks in some special cases, as well as \(\mathbf {B}^\wedge \mathbf {B}^\vee \)-networks.
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Assistance of A. M. Cegarra is deeply appreciated.
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Communicated by Làszló Márki.
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Petrich, M. On some intervals of varieties of completely regular semigroups. Semigroup Forum 100, 513–541 (2020). https://doi.org/10.1007/s00233-019-10053-w
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DOI: https://doi.org/10.1007/s00233-019-10053-w