The [0-Simple] Simple Subsemigroups of Nonnegative Matrices

In this paper, we investigate the properties of the [0-simple] simple subsemigroups of nonnegative matrices and show that the [0-simple] simple subsemigroups of Mn(S) are completely [0-simple] simple, where S is a strong ideal subset of R+ which has no ele- ments less than 1 except 0. Finally, we illustrate that the semigroup of nonnegative matriles is interesting.