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 A is not a permutation matrix and if A=BC then B or C must be a permutation matrix. Sufficient conditions for A to be prime are given.
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References
De de Caen, Prime Boolean Matrices, Master’s Thesis, Queen’s University at Kingston (1979).
J. Borosh, D.J. Hartfiel and C.J. Maxson, Answers to Questions posed by Richman and Schneider, Linear and Multilinear Algebra 3 (1976), 255–258.
D.J. Richman and H. Schneider, Primes in the Semigroup of Non-negative Matrices, Linear and Multilinear Algebra 2 (1974), 135–140.
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© 1980 Springer-Verlag
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De Caen, D., Gregory, D.A. (1980). Prime boolean matrices. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088902
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DOI: https://doi.org/10.1007/BFb0088902
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