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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