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

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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. 
@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},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a4/}
}
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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/