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.

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 $\mathrm{GL}_3(\mathbb F)$. 
@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/}
}
TY  - JOUR
AU  - E. I. Bunina
AU  - V. V. Nemiro
TI  - The group of fractions of the semigroup of invertible nonnegative matrices of order three over a~field
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 27
EP  - 42
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a2/
LA  - ru
ID  - FPM_2013_18_3_a2
ER  - 
%0 Journal Article
%A E. I. Bunina
%A V. V. Nemiro
%T The group of fractions of the semigroup of invertible nonnegative matrices of order three over a~field
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 27-42
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a2/
%G ru
%F FPM_2013_18_3_a2
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/

[1] Bunina E. I., “Avtomorfizmy polugruppy neotritsatelnykh obratimykh matrits poryadka dva nad chastichno uporyadochennymi kommutativnymi koltsami”, Mat. zametki, 91:1 (2012), 3–11 | DOI | Zbl

[2] Bunina E. I., Mikhalëv A. V., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami”, Fundament. i prikl. mat., 11:2 (2005), 3–23 | MR | Zbl

[3] Bunina E. I., Mikhalëv A. V., “Elementarnaya ekvivalentnost polugruppy obratimykh matrits s neotritsatelnymi elementami”, Fundament. i prikl. mat., 12:2 (2006), 39–53 | MR | Zbl

[4] Bunina E. I., Semënov P. P., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami nad chastichno uporyadochennymi koltsami”, Fundament. i prikl. mat., 14:2 (2008), 69–100 | MR | Zbl

[5] Bunina E. I., Semënov P. P., “Elementarnaya ekvivalentnost polugruppy obratimykh matrits s neotritsatelnymi elementami nad chastichno uporyadochennymi koltsami”, Fundament. i prikl. mat., 14:4 (2008), 75–85 | MR

[6] Maltsev A. I., “O vklyuchenii assotsiativnykh sistem v gruppy. II”, Mat. sb., 8(50):2 (1940), 251–264 | MR | Zbl

[7] Mikhalëv A. V., Shatalova M. A., “Avtomorfizmy i antiavtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami”, Mat. sb., 81(123):4 (1970), 600–609 | MR | Zbl

[8] Semënov P. P., “Endomorfizmy polugrupp obratimykh neotritsatelnykh matrits nad uporyadochennymi koltsami”, Fundament. i prikl. mat., 17:5 (2011/2012), 165–178 | MR

[9] Semënov P. P., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi tselymi elementami”, Mat. sb., 203:9 (2012), 117–132 | DOI | MR | Zbl

[10] Fayans V. G., “Gruppa chastnykh polugruppy neosobennykh matrits s neotritsatelnymi elementami”, Uspekhi mat. nauk, 28:6 (1973), 221–222 | MR | Zbl