Primes in the semigroup of non-negative matrices

  title={Primes in the semigroup of non-negative matrices},
  author={Daniel J. Richman and Hans Schneider},
A matrix A in the semigroup N n of non-negative n×nmatrices is prime if A is not monomial and A=BC,B CeN n implies that either B or C is monomial. One necessary and another sufficient condition are given for a matrix in N n to be prime. It is proved that every prime in N n is completely decomposable.