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On the variety of bands in completely regular semigroups. (English) Zbl 1389.20067

In a number of recent papers, the author has explored the complete congruences \(\mathbf{B}^\wedge\) and \(\mathbf{B}^\vee\) on the lattice \(\mathcal{L(CR)}\) of varieties of completely regular semigroups obtained, respectively, by meeting and joining with the variety \(\mathcal{B}\) of bands. It is shown here that each \(\mathbf{B}^\vee\)-class is embeddable into the ideal of \(\mathcal{L(CR)}\) generated by \(\mathcal{B}\). Another theorem determines the quotient modulo \(\mathbf{B}^\vee\) of the ideal of \(\mathcal{L(CR)}\) generated by the variety of completely simple semigroups.

MSC:

20M07 Varieties and pseudovarieties of semigroups
20M10 General structure theory for semigroups
20M17 Regular semigroups
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