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Regular version of the site

Article

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

Journal of Mathematical Sciences. 2013. Vol. 193. No. 5. P. 802-808.
Shitov Y.

We consider the rank functions of matrices over semirings, 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.