The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field

E. I. Bunina; V. V. Nemiro

The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field

E. I. Bunina, V. V. Nemiro

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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)	27-42
Number of pages	16
Journal	Fundamental and Applied Mathematics
Volume	18
Issue number	3
State	Published - 2013

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Cite this

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title = "The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field",

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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N2 - 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).

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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M3 - مقالة

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JO - Fundamental and Applied Mathematics

JF - Fundamental and Applied Mathematics

IS - 3

ER -

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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