The lattices of varieties and pseudovarieties of band monoids (Q1074725)

From the well-known lattice \({\mathcal L}{\mathcal B}\) of varieties of bands (e.g. \textit{C. Fennemore} [Semigroup Forum 1, 172-179 (1970; Zbl 0206.304)]) the author determines the lattice \({\mathcal L}{\mathcal B}{\mathcal M}\) of varieties of band monoids. She does this by analyzing the congruence on \({\mathcal L}{\mathcal B}\) induced by the homomorphism which associates, with any variety V of bands, the variety \(V\cap M\) of band monoids consisting of the monoids in V. The lattice \({\mathcal L}{\mathcal B}{\mathcal M}\) has a very simple structure. It is also shown that the lattice \({\mathcal L}{\mathcal B}{\mathcal M}\) is isomorphic with the lattice \({\mathcal L}{\mathcal F}{\mathcal B}{\mathcal M}\) of pseudovarieties of finite band monoids.