Open Access
2009 Faithful linear representations of bands
F. Cedó, J. Okniński
Publ. Mat. 53(1): 119-140 (2009).


A band is a semigroup consisting of idempotents. It is proved that for any field $K$ and any band $S$ with finitely many components, the semigroup algebra $K[S]$ can be embedded in upper triangular matrices over a commutative $K$-algebra. The proof of a theorem of Malcev on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if $S=F\cup E$ is a band with two components $E$, $F$ such that $F$ is an ideal of $S$ and $E$ is finite, then $S$ is a linear semigroup. Certain sufficient conditions for linearity of a band $S$, expressed in terms of annihilators associated to $S$, are also obtained.


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F. Cedó. J. Okniński. "Faithful linear representations of bands." Publ. Mat. 53 (1) 119 - 140, 2009.


Published: 2009
First available in Project Euclid: 17 December 2008

zbMATH: 1178.20054
MathSciNet: MR2474118

Primary: 16R20 , 16S36 , 20M25
Secondary: 20M12 , 20M17 , 20M30

Keywords: annihilator , Linear band , normal band , PI rings , semigroup algebra , triangular matrices

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 1 • 2009
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