In
mathematics, a
band (also called
idempotent semigroup) is a
semigroup in which every element is
idempotent (in other words equal to its own square). Bands were first studied and named by ; the
lattice of
varieties of bands was described independently in the early 1970s by Biryukov, Fennemore and Gerhard.
Semilattices,
left-zero bands,
right-zero bands,
rectangular bands,
normal bands,
left-regular bands,
right-regular 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.