Geodesic
Extension of endomorphisms of the subsemigroup $\mathrm{GE}^+_2(R)$ to endomorphisms of $\mathrm{GE}^+_2(R[x])$, where~$R$ is a~partially-ordered commutative ring without zero divisors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 155-184.

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Let $R$ be a partially ordered commutative ring without zero divisors, $G_n(R)$ be the subsemigroup of $\mathrm{GL}_n(R)$ consisting of matrices with nonnegative elements, and $\mathrm{GE}^+_n(R)$ be its subsemigroup generated by elementary transformation matrices, diagonal matrices, and permutation matrices. In this paper, we describe in which cases endomorphisms of $\mathrm{GE}^+_2(R)$ can be extended to endomorphisms of $\mathrm{GE}^+_2(R[x])$. 
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     author = {O. I. Tsarkov},
     title = {Extension of endomorphisms of the subsemigroup $\mathrm{GE}^+_2(R)$ to endomorphisms of $\mathrm{GE}^+_2(R[x])$, where~$R$ is a~partially-ordered commutative ring without zero divisors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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O. I. Tsarkov. Extension of endomorphisms of the subsemigroup $\mathrm{GE}^+_2(R)$ to endomorphisms of $\mathrm{GE}^+_2(R[x])$, where~$R$ is a~partially-ordered commutative ring without zero divisors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 155-184. http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a11/

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