Geodesic
The group of quotients of the semigroup of invertible nonnegative matrices over local rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 167-188

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In this paper, we prove that for a linearly ordered local ring $R$ with $1/2$ the group of quotients of the semigroup of invertible nonnegative matrices $\mathrm G_n(R)$ for $n \geq 3$ coincides with the group $\mathrm{GL}_n(R)$. 
@article{FPM_2019_22_4_a11,
     author = {V. V. Nemiro},
     title = {The group of quotients of the semigroup of invertible nonnegative matrices over local rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {167--188},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a11/}
}
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V. V. Nemiro. The group of quotients of the semigroup of invertible nonnegative matrices over local rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 167-188. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a11/