Faithful linear representations of bands
Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Okniński, Jan (Warsaw University (Polònia). Institute of Mathematics)

Data:	2009
Resum:	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 [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ 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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Linear band ; Semigroup algebra ; Triangular matrices ; Annihilator ; PI rings ; Normal band
Publicat a:	Publicacions matemàtiques, V. 53 n. 1 (2009) p. 119-140, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/140650
DOI: 10.5565/PUBLMAT_53109_06

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