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Band (mathematics)
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.
==Varieties of bands==
A class of bands forms a variety if it is closed under formation of subsemigroups, homomorphic images and direct product. Each variety of bands can be defined by a single defining identity.〔.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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