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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - V. V. Nemiro
TI  - The group of quotients of the semigroup of invertible nonnegative matrices over local rings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2019
SP  - 167
EP  - 188
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a11/
LA  - ru
ID  - FPM_2019_22_4_a11
ER  - 
%0 Journal Article
%A V. V. Nemiro
%T The group of quotients of the semigroup of invertible nonnegative matrices over local rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2019
%P 167-188
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a11/
%G ru
%F FPM_2019_22_4_a11
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/

[1] Bunina E. I., “Avtomorfizmy polugruppy neotritsatelnykh obratimykh matrits poryadka dva nad chastichno uporyadochennymi kommutativnymi koltsami”, Matem. zametki, 91:1 (2011), 3–12

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

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

[4] Bunina E. I., Mikhalev A. V., Nemiro V. V., “Gruppy chastnykh polugrupp obratimykh neotritsatelnykh matrits nad telami”, Dokl. RAN, 472:2 (2017), 1–4

[5] Bunina E. I., Nemiro V. V., “Gruppa chastnykh polugruppy obratimykh neotritsatelnykh matrits poryadka tri nad polyami”, Fundament. i prikl. matem., 18:3 (2013), 27–42 | MR

[6] Bunina E. I., Semenov P. P., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami nad chastichno uporyadochennymi koltsami”, Fundament. i prikl. matem., 14:2 (2008), 69–100

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

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

[9] Mikhalev A. V., Shatalova M. A., “Avtomorfizmy i antiavtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami”, Matem. sb., 81:4 (1970), 600–609 | Zbl

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

[11] Semenov P. P., “Endomorfizmy polugrupp obratimykh neotritsatelnykh matrits nad uporyadochennymi koltsami”, Fundament. i prikl. matem., 17:5 (2012), 165–178

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