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.

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