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
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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 $\mathrm{GL}_3(\mathbb F)$.
@article{FPM_2013_18_3_a2,
author = {E. I. Bunina and V. V. Nemiro},
title = {The group of fractions of the semigroup of invertible nonnegative matrices of order three over a~field},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {27--42},
publisher = {mathdoc},
volume = {18},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a2/}
}
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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/