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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathrm{GE}^+_2(R[x])$. 
@article{FPM_2013_18_4_a11,
     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},
     pages = {155--184},
     year = {2013},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a11/}
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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/

[1] Bunina E. I., “Avtomorfizmy polugruppy neotritsatelnykh obratimykh matrits poryadka dva nad chastichno uporyadochennymi kommutativnymi koltsami”, Mat. zametki, 91:1 (2011), 3–12 | DOI

[2] Bunina E. I., Mikhalëv A. V., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami”, Fundament. i prikl. mat., 11:2 (2005), 3–23 | MR | Zbl

[3] Bunina E. I., Mikhalëv A. V., “Elementarnaya ekvivalentnost polugruppy obratimykh matrits s neotritsatelnymi elementami”, Fundament. i prikl. mat., 12:2 (2006), 39–53 | MR | Zbl

[4] Bunina E. I., Semënov P. P., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami nad chastichno uporyadochennymi koltsami”, Fundament. i prikl. mat., 14:2 (2008), 69–100 | MR | Zbl

[5] Bunina E. I., Semënov P. P., “Elementarnaya ekvivalentnost polugruppy obratimykh matrits s neotritsatelnymi elementami nad chastichno uporyadochennymi koltsami”, Fundament. i prikl. mat., 14:4 (2008), 75–85 | MR

[6] Mikhalëv A. V., Shatalova M. A., “Avtomorfizmy i antiavtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi elementami”, Mat. sb., 81(123):4 (1970), 600–609 | MR | Zbl

[7] Semënov P. P., “Avtomorfizmy polugruppy obratimykh matrits s neotritsatelnymi tselymi elementami”, Mat. sb., 203:9 (2012), 117–132 | DOI | MR | Zbl

[8] Tsarkov O. I., “Endomorfizmy polugruppy $G_2(R)$ nad chastichno uporyadochennym kommutativnym koltsom bez delitelei nulya s 1/2”, Fundament. i prikl. mat., 18:1 (2013), 181–204