Geodesic
Endomorphisms of the semigroup $G_2(R)$ over partially ordered commutative rings without zero divisors and with~$1/2$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 1, pp. 181-204.

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Let $R$ be a partially ordered commutative ring without zero divisors and with $1/2$. Let $G_n(R)$ be the subsemigroup of $\mathrm{GL}_n(R)$ consisting of matrices with nonnegative elements. In the paper, we describe endomorphisms of this semigroup for $n=2$. 
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O. I. Tsarkov. Endomorphisms of the semigroup $G_2(R)$ over partially ordered commutative rings without zero divisors and with~$1/2$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 1, pp. 181-204. http://geodesic.mathdoc.fr/item/FPM_2013_18_1_a10/

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