Faithful linear representations of bands
Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Okniński, Jan (Warsaw University (Polònia). Institute of Mathematics)
Date: |
2009 |
Abstract: |
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. |
Rights: |
Tots els drets reservats. |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Subject: |
Linear band ;
Semigroup algebra ;
Triangular matrices ;
Annihilator ;
PI rings ;
Normal band |
Published in: |
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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Record created 2009-10-15, last modified 2022-02-13