Prlmes In the Semlgroup of Boolean Matrlces
D. de Caen, David Alexander Gregory · 1981
Let A, B, C be R X n matrices of zeros and ones. Using Boolean addition and multiplication, we say that A is prime if it is not a permutation matrix and if A =BC implies that B or C must be a permutation matrix. Conditions sufficient for a matrix to be prime are provided, and a characterization of primes in terms of a notion of rank is given. Finally, an order property of primes is used to obtain a result on prime factors.