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Fundamentalnaya i Prikladnaya Matematika, 2013, Volume 18, Issue 3, Pages 27–42
(Mi fpm1514)
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This article is cited in 3 scientific papers (total in 3 papers)
The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field
E. I. Bunina, V. V. Nemiro Lomonosov Moscow State University, Moscow, Russia
Abstract:
Let $\mathbb F$ be a linearly ordered field. Consider $\mathrm G_n(\mathbb F)$, which is the subsemigroup of $\mathrm{GL}_n(\mathbb F)$ consisting of all matrices with nonnegative coefficients. In 1940, A. I. Maltsev introduced the concept of the group of fractions for a semigroup. In the given paper, we prove that the group of fractions of $\mathrm G_3(\mathbb F)$ coincides with $\mathrm{GL}_3(\mathbb F)$.
Citation:
E. I. Bunina, V. V. Nemiro, “The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field”, Fundam. Prikl. Mat., 18:3 (2013), 27–42; J. Math. Sci., 206:5 (2015), 474–485
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https://www.mathnet.ru/eng/fpm1514 https://www.mathnet.ru/eng/fpm/v18/i3/p27
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Abstract page: | 306 | Full-text PDF : | 137 | References: | 51 | First page: | 2 |
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