Zero-Term Rank Inequalities and Their Extreme Preservers

Seok-Zun Song, Seong-Hee Heo

The zero-term rank of a matrix $A$ over a semiring $\Cal S$ is the least number of lines (rows or columns) needed to include all the zero entries in $A$. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to zero-term rank inequalities of matrices over nonbinary Boolean algebras.