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 Fundam. Prikl. Mat., 2013, Volume 18, Issue 4, Pages 155–184 (Mi fpm1536)

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

O. I. Tsarkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2015, 206:6, 711–733

Bibliographic databases:

UDC: 512.55+512.64

Citation: 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”, Fundam. Prikl. Mat., 18:4 (2013), 155–184; J. Math. Sci., 206:6 (2015), 711–733

Citation in format AMSBIB
\Bibitem{Tsa13} \by O.~I.~Tsarkov \paper 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 \jour Fundam. Prikl. Mat. \yr 2013 \vol 18 \issue 4 \pages 155--184 \mathnet{http://mi.mathnet.ru/fpm1536} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431839} \transl \jour J. Math. Sci. \yr 2015 \vol 206 \issue 6 \pages 711--733 \crossref{https://doi.org/10.1007/s10958-015-2348-y} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84956766203}