Original Article
Kyungpook Mathematical Journal 2013; 53(2): 273-283
Published online June 23, 2013
Copyright © Kyungpook Mathematical Journal.
Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers
Seok-Zun Song1, Young-Bae Jun2
1Department of Mathematics, Jeju National University, Jeju 690-756, Republic of Korea
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Republic of Korea
In this paper, we consider the row rank inequalities derived from comparisons of the row ranks of the additions and multiplications of nonnegative integer matrices and construct the sets of nonnegative integer matrix pairs which is occurred at the extreme cases for the row rank inequalities. We characterize the linear operators that preserve these extreme sets of nonnegative integer matrix pairs.
Keywords: semiring, linear operator, row rank, $(P,Q)$-operator