• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero 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 term rank inequalities of matrices over nonbinary Boolean semirings.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.531-540
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• 1995

There is much literature on the study of matrices over a finite Boolean algebra. But many results in Boolean matrix theory are stated only for binary Boolean matrices. This is due in part to a semiring isomorphism between the matrices over the Boolean algebra of subsets of a k element set and the k tuples of binary Boolean matrices. This isomorphism allows many questions concerning matrices over an arbitrary finite Boolean algebra to be answered using the binary Boolean case. However there are interesting results about the general (i.e. nonbinary) Boolean matrices that have not been mentioned and they differ somwhat from the binary case.