Primes in the semigroup of Boolean matrices |
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Authors: | D. de Caen D.A. Gregory |
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Affiliation: | University of Toronto Toronto, Ontario, Canada;Queen''s University Kingston, Ontario, Canada |
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Abstract: | Let A, B, C be n×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 nation of rank is given. Finally, an order property of primes is used to obtain a result on prime factors. |
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