Geodesic
Automorphisms of the semigroup of invertible matrices with nonnegative elements
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 3-23

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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. 
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     author = {E. I. Bunina and A. V. Mikhalev},
     title = {Automorphisms of the semigroup of invertible matrices with nonnegative elements},
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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/