Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2013; 28(1): 1-9

Printed January 31, 2013

https://doi.org/10.4134/CKMS.2013.28.1.1

Copyright © The Korean Mathematical Society.

Extreme sets of rank inequalities over Boolean matrices and their preservers

Seok Zun Song, Mun-Hwan Kang, and Young Bae Jun

Jeju National University, Jeju National University, Gyeongsang National University

Abstract

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We consider the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X) = PXP^{T} $ with some permutation matrix $P$.

Keywords: linear operator, Boolean rank inequality, $(P,Q,B)$-operator, nonbinary Boolean algebra

MSC numbers: Primary 15A86, 15A03, 15A04

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