Geodesic
Automorphisms of the semigroup of invertible matrices with nonnegative elements
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 3-23 
E. I. Bunina; A. V. Mikhalev. Automorphisms of the semigroup of invertible matrices with nonnegative elements. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly ordered associative ring on some specially defined subgroup coincides with the composition of an inner automorphism of the semigroup, an order-preserving automorphism of the ring, and a central homothety.

[1] Ilin S. N., “Obratimye matritsy nad (neassotsiativnymi) antikoltsami”, Universalnaya algebra i eë prilozheniya, Peremena, Volgograd, 2000, 81–89

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