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 ; publishedVersion
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 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_53109_06
DOI: 10.5565/140650

22 p, 215.4 KB

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