FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 3, PAGES 27-42

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

E. I. Bunina
V. V. Nemiro

Abstract

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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 $G$₃(F) coincides with $GL$₃(F).

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Last modified: March 4, 2014