I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 6, PAGES 223-232
Ya. N. Shitov
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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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Last modified: November 21, 2012