FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 6, PAGES 223-232

**On the coincidence of the factor and Gondran--Minoux rank functions of
matrices over a semiring**

Ya. N. Shitov

Abstract

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We consider the rank functions of matrices over semiring, functions
that generalize the classical notion of the rank of a matrix over
a field.
We study semirings over which the factor and Gondran--Minoux ranks of
any matrix coincide.
It is shown that every semiring satisfying that condition is
a subsemiring of a field.
We provide an example of an integral domain over which the factor and
Gondran--Minoux ranks are different.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k116/k11607h.htm

Last modified: November 21, 2012