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Fundamentalnaya i Prikladnaya Matematika, 2013, Volume 18, Issue 4, Pages 155–184
(Mi fpm1536)
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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 $\mathrm{GE}^+_2(R[x])$.
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
Linking options:
https://www.mathnet.ru/eng/fpm1536 https://www.mathnet.ru/eng/fpm/v18/i4/p155
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Abstract page: | 209 | Full-text PDF : | 98 | References: | 38 |
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