Bremner, Murray R.; El Bachraoui, Mohamed On the semigroup algebra of binary relations. (English) Zbl 1213.20064 Commun. Algebra 38, No. 9, 3499-3505 (2010). Summary: The semigroup of binary relations on \(\{1,\dots,n\}\) with the relative product is isomorphic to the semigroup \(B_n\) of \(n\times n\) 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 \(M_{2^n-1}(F)\). Cited in 2 Documents MSC: 20M20 Semigroups of transformations, relations, partitions, etc. 20M25 Semigroup rings, multiplicative semigroups of rings 15B34 Boolean and Hadamard matrices 03G15 Cylindric and polyadic algebras; relation algebras 16S36 Ordinary and skew polynomial rings and semigroup rings 20M30 Representation of semigroups; actions of semigroups on sets Keywords:semigroups of binary relations; Boolean matrices; representation theory; semigroup algebras; semigroups of matrices PDFBibTeX XMLCite \textit{M. R. Bremner} and \textit{M. El Bachraoui}, Commun. Algebra 38, No. 9, 3499--3505 (2010; Zbl 1213.20064) Full Text: DOI References: [1] Clifton J. M., Proc. Amer. Math. Soc. 83 pp 248– (1981) [2] DOI: 10.1090/S0002-9939-1977-0444823-9 · doi:10.1090/S0002-9939-1977-0444823-9 [3] Schwarz S., Czechoslovak Math. J. 20 pp 632– (1970) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.