Biordered set

A biordered set (otherwise known as boset) is a mathematical object that occurs in the description of the structure of the set of idempotents in a semigroup.

The set of idempotents in a semigroup is a biordered set and every biordered set is the set of idempotents of some semigroup.[1][2] A regular biordered set is a biordered set with an additional property. The set of idempotents in a regular semigroup is a regular biordered set, and every regular biordered set is the set of idempotents of some regular semigroup.[1]

  1. ^ a b Cite error: The named reference namb was invoked but never defined (see the help page).
  2. ^ Easdown, David (1985). "Biordered sets come from semigroups". Journal of Algebra. 96 (2): 581–91. doi:10.1016/0021-8693(85)90028-6.