Geodesic
The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 27-42 
E. I. Bunina; V. V. Nemiro. The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 27-42. http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathbb F$ be a linearly ordered field. Consider $\mathrm G_n(\mathbb F)$, which is the subsemigroup of $\mathrm{GL}_n(\mathbb F)$ consisting of all matrices with nonnegative coefficients. In 1940, A. I. Maltsev introduced the concept of the group of fractions for a semigroup. In the given paper, we prove that the group of fractions of $\mathrm G_3(\mathbb F)$ coincides with $\mathrm{GL}_3(\mathbb F)$.

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