Petrich, Mario On the variety of bands in completely regular semigroups. (English) Zbl 1389.20067 Publ. Math. Debr. 89, No. 1-2, 43-61 (2016). 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. Reviewer: Peter R. Jones (Milwaukee) MSC: 20M07 Varieties and pseudovarieties of semigroups 20M10 General structure theory for semigroups 20M17 Regular semigroups Keywords:semigroup; completely regular semigroup; completely simple semigroup; band; variety; relation; operator PDFBibTeX XMLCite \textit{M. Petrich}, Publ. Math. Debr. 89, No. 1--2, 43--61 (2016; Zbl 1389.20067) Full Text: DOI