Faithful linear representations of bands

Ferran Cedó, Jan Okniński

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)119-140
JournalPublicacions Matematiques
Volume53
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Annihilator
  • Linear band
  • Normal band
  • PI rings
  • Semigroup algebra
  • Triangular matrices

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