Rings Associated to Bands with Two Components
Ferran Cedó, Elena Rodríguez-Jorge · Communications in Algebra · 2010
A band is a semigroup whose elements are idempotents. It is proved that for any field K the commutative K-algebra, constructed in [2 Cedó , F. , Okniński , J. ( 2009 ). Faithful linear representations of bands . Publ. Mat. 53 : 119 – 140 . [Google Scholar]], associated to a band S with two components E, F such that EFE = F, is a reduced ring. Thus the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative reduced K-algebra.