The Group of Fractions of the Semigroup of Invertible Nonnegative Matrices of Order Three Over a Field

E. I. Bunina; V. V. Nemiro

doi:10.1007/s10958-015-2326-4

The Group of Fractions of the Semigroup of Invertible Nonnegative Matrices of Order Three Over a Field

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Abstract

Let F be a linearly ordered field. Consider G_n(F), which is the subsemigroup of GL_n(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 G₃(F) coincides with GL₃(F).

Original language	English
Pages (from-to)	474-485
Number of pages	12
Journal	Journal of Mathematical Sciences
Volume	206
Issue number	5
DOIs	https://doi.org/10.1007/s10958-015-2326-4
State	Published - 1 May 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-015-2326-4

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abstract = "Let F be a linearly ordered field. Consider Gn(F), which is the subsemigroup of GLn(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 G3(F) coincides with GL3(F).",

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AB - Let F be a linearly ordered field. Consider Gn(F), which is the subsemigroup of GLn(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 G3(F) coincides with GL3(F).

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The Group of Fractions of the Semigroup of Invertible Nonnegative Matrices of Order Three Over a Field

Abstract

All Science Journal Classification (ASJC) codes

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