Linear Representations of Semigroups of Boolean Matrices
Linear Representations of Semigroups of Boolean Matrices
Let Bn be the multiplicative semigroup of n x n matrices over the semiring 0, 1 under the operations "or" and "and".We show that the least possible degree of a faithful representation of Bn over a field is 2" -1 by studying representations of a subsemigroup of Bn.By different methods …