FPM 2013, vol. 18, no. 4, pp. 155-

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 4, PAGES 155-

Extension of endomorphisms of the subsemigroup $GE$ ⁺₂(R) to endomorphisms of $GE$ ⁺₂(R[x]), where $R$ is a partially-ordered commutative ring without zero divisors

O. I. Tsarkov

Abstract

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Let $R$ be a partially ordered commutative ring without zero divisors, $G$ _n(R) be the subsemigroup of $GL$ _n(R) consisting of matrices with nonnegative elements, and $GE$ ⁺_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 $GE$ ⁺₂(R) can be extended to endomorphisms of $GE$ ⁺₂(R[x]).

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Extension of endomorphisms of the subsemigroup GE+2(R) to endomorphisms of GE+2(R[x]), where R is a partially-ordered commutative ring without zero divisors

Extension of endomorphisms of the subsemigroup $GE$ ⁺₂(R) to endomorphisms of $GE$ ⁺₂(R[x]), where $R$ is a partially-ordered commutative ring without zero divisors