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- Title
Characterizations of Zero-Term Rank Preservers of Matrices over Semirings.
- Authors
KYUNG-TAE KANG; SEOK-ZUN SONG; BEASLEY, LEROY B.; HERNANDEZ ENCINAS, LUIS
- Abstract
Let M(5) denote the set of all mxn matrices over a semiring S. For A ∈ M (S), zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on M(S) preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on M(S) that preserve zero-term rank. Consequently we obtain that a linear operator on M(S) preserves zero-term rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where 0 ≤ k ≤ min{m, n} - 1 if and only if it strongly preserves zero-term rank h, where 1 ≤ h ≤ min{m, n}.
- Subjects
MATRICES (Mathematics); SEMIRINGS (Mathematics); LINEAR operators; NUMBER systems; GROUP theory
- Publication
Kyungpook Mathematical Journal, 2014, Vol 54, Issue 4, p619
- ISSN
1225-6951
- Publication type
Article
- DOI
10.5666/KMJ.2014.54.4.619