Geodesic
Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 75-85 
E. I. Bunina; P. P. Semenov. Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 75-85. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a4/
@article{FPM_2008_14_4_a4,
     author = {E. I. Bunina and P. P. Semenov},
     title = {Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {75--85},
     year = {2008},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a4/}
}
TY  - JOUR
AU  - E. I. Bunina
AU  - P. P. Semenov
TI  - Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 75
EP  - 85
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a4/
LA  - ru
ID  - FPM_2008_14_4_a4
ER  - 
%0 Journal Article
%A E. I. Bunina
%A P. P. Semenov
%T Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 75-85
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a4/
%G ru
%F FPM_2008_14_4_a4

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

In the paper we prove that if two semigroups of invertible matrices with nonnegative elements over partially ordered commutative rings are elementarily equivalent, then their dimensions coincide and the corresponding semirings of nonnegative elements are elementarily equivalent.

[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”, Fundament. i prikl. mat., 4:4 (1998), 1265–1278 | MR | Zbl

[3] Bunina E. I., “Elementarnye svoistva grupp Shevalle nad lokalnymi koltsami”, Uspekhi mat. nauk, 61:2 (2006), 157–158 | MR | Zbl

[4] Bunina E. I., “Elementarnaya ekvivalentnost grupp Shevalle nad polyami”, Fundament. i prikl. mat., 12:8 (2006), 29–77 | MR

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

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

[7] 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

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

[9] 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

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