On the semigroup algebra of binary relations

Murray R. Bremner, Mohamed El Bachraoui

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The semigroup of binary relations on {1,. . .;., n} with the relative product is isomorphic to the semigroup Bn of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FBn contains an ideal Kn of dimension (2n-1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n-1(F).

Original languageEnglish
Pages (from-to)3499-3505
Number of pages7
JournalCommunications in Algebra
Issue number9
Publication statusPublished - 2010
Externally publishedYes


  • Binary relations
  • Boolean matrices
  • Representational theory
  • Semigroup algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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