Geodesic
Elementary equivalence of the semigroup of invertible matrices with nonnegative elements
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 39-53.

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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. 
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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/

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