Wismath, S. L. The lattice of varieties of *-regular band monoids. (English) Zbl 0767.20023 Semigroup Forum 46, No. 1, 130-133 (1993). A \(*\)-regular band is a band equipped with an involution \(x\to x^*\) that satisfies \(xx^*x = x\). In this short note, the author finds all varieties of *-regular band monoids, in a similar fashion to her description [ibid. 33, 187-198 (1986; Zbl 0591.20060)] of all varieties of band monoids. The lattice is obtained from the natural numbers (under the usual order) by adjoining an identity at the top and a four-element diamond at the bottom. Reviewer: P.R.Jones (Milwaukee) Cited in 1 Document MSC: 20M07 Varieties and pseudovarieties of semigroups 08B15 Lattices of varieties Keywords:involution; varieties of \(*\)-regular band monoids; lattice Citations:Zbl 0591.20060 PDFBibTeX XMLCite \textit{S. L. Wismath}, Semigroup Forum 46, No. 1, 130--133 (1993; Zbl 0767.20023) Full Text: DOI EuDML References: [1] Adair, C. L.,Bands with Involution, J. Algebra75 (1982), 297–314. · Zbl 0501.20040 · doi:10.1016/0021-8693(82)90042-4 [2] Birjukov, A. P.,The lattice of varieties of idempotent semigroups, All-Union Colloquium on General Algebra, Riga (1967), 16–18. [3] Fennemore, C.,All varieties of bands, Math. Nachr.48 (1971), 237–262. · Zbl 0194.02801 · doi:10.1002/mana.19710480118 [4] Gerhard, J. A.,The lattice of equational classes of idempotent semigroups, J. Algebra15 (1970), 195–224. · Zbl 0194.02701 · doi:10.1016/0021-8693(70)90073-6 [5] Wismath, S. L.,The Lattices of Varieties and Pseudovarieties of Band Monoids, Semigroup Forum33 (1986), 187–198. · Zbl 0591.20060 · doi:10.1007/BF02573192 [6] Wismath, S. L.,The Lattices of Varieties and Pseudovarieties of Band Monoids, M.Sc. Thesis, Simon Fraser University, 1983. · Zbl 0591.20060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.