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).

Location: http://mech.math.msu.su/~fpm/eng/k13/k133/k13303h.htm

Last modified: March 4, 2014