In
mathematics, a band is a
semigroup in which every element is
idempotent (in other words equal to its own square). The
lattice of
varieties of bands was described independently by Birjukov, Fennemore and Gerhard. Semilattices, left-zero bands, right-zero bands, rectangular bands and regular bands, specific subclasses of bands which lie near the bottom of this lattice, are of particular interest and are briefly described below. Bands have found applications in various branches of mathematics, notably in
theoretical computer science.
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