On the Semigroup Algebra of Binary Relations |
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| Authors: | Murray R. Bremner Mohamed El Bachraoui |
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| Affiliation: | 1. Department of Mathematics and Statistics , University of Saskatchewan , Saskatoon, Canada bremner@math.usask.ca;3. School of Science and Engineering , Al-Akhawayn University , Ifrane, Morocco |
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| Abstract: | The semigroup of binary relations on {1,…, n} with the relative product is isomorphic to the semigroup B n of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FB n contains an ideal K n of dimension (2 n ? 1)2, and we construct an explicit isomorphism of K n with the matrix algebra M 2 n ?1(F). |
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| Keywords: | Binary relations Boolean matrices Representational theory Semigroup algebras |
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