Abstract
Adair determined the lattice of varieties of *-bands and provided a single identity for each of them. We construct a new set of identities for the same purpose. Both of these systems involve at least one variable which is starred. Using the second system of identities, we show that the system of identities constructed by Gerhard and the author for varieties of bands also represents a set of identities determining the varieties of *-bands. The same type of result is proved for varieties of band monoids and varieties of *-band monoids using the results of two papers by Wismath.
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Petrich, M. Identities without the star for *-bands. Algebra Universalis 36, 46–65 (1996). https://doi.org/10.1007/BF01192708
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DOI: https://doi.org/10.1007/BF01192708