Geodesic
Elementary equivalence of the semigroup of invertible matrices with nonnegative elements
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 39-53
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we prove that the semigroups of invertible matrices with nonnegative elements over linearly ordered associative rings are elementarily equivalent if and only if the matrices have the same dimension and the rings are elementarily equivalent as ordered rings. 
@article{FPM_2006_12_2_a2,
     author = {E. I. Bunina and A. V. Mikhalev},
     title = {Elementary equivalence of the semigroup of invertible matrices with nonnegative elements},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {39--53},
     year = {2006},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a2/}
}
TY  - JOUR
AU  - E. I. Bunina
AU  - A. V. Mikhalev
TI  - Elementary equivalence of the semigroup of invertible matrices with nonnegative elements
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 39
EP  - 53
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a2/
LA  - ru
ID  - FPM_2006_12_2_a2
ER  - 
%0 Journal Article
%A E. I. Bunina
%A A. V. Mikhalev
%T Elementary equivalence of the semigroup of invertible matrices with nonnegative elements
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 39-53
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a2/
%G ru
%F FPM_2006_12_2_a2
E. I. Bunina; A. V. Mikhalev. Elementary equivalence of the semigroup of invertible matrices with nonnegative elements. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 39-53. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a2/

[1] Bunina E. I., “Elementarnaya ekvivalentnost unitarnykh lineinykh grupp nad koltsami i telami”, Uspekhi mat. nauk, 53:2 (1998), 137–138 | MR | Zbl

[2] Bunina E. I., “Elementarnaya ekvivalentnost unitarnykh lineinykh grupp nad polyami”, Fundam. i prikl. mat., 4:4 (1998), 1265–1278 | MR | Zbl

[3] Bunina E. I., “Gruppy Shevalle nad polyami i ikh elementarnye svoistva”, Uspekhi mat. nauk., 59:5 (2004), 952–953 | MR | Zbl

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

[5] Maltsev A. I., “Ob elementarnykh svoistvakh lineinykh grupp”, Problemy matematiki i mekhaniki, Novosibirsk, 1961, 110–132

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

[7] Beidar C. I., Mikhalev A. V., “On Malcev's theorem on elementary equivalence of linear groups”, Contemp. Math., 131 (1992), 29–35 | MR | Zbl