Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 1996; 33(3): 335-342

Published online September 1, 1996

Copyright © The Korean Mathematical Society.

Domination preserving linear operators over semirings

Gwang-Yeon Lee and Hang-Kyun Shin

Hanseo University and Woosuk University

Abstract

Let $\Cal S$ be any semiring and ${\Cal M}(\Cal S )$ be the set of all $m\times n$ matrices over $\Cal S$. If linear operator $T$ is a term rank preserver, then $T$ is a very useful operator for characterization of various preservers on ${\Cal M(S)}$. The linear operator $T$ is called a domination preserving operator if $T(A)\le T(B)$ for $A\le B$. In this paper, we proved that $T$ is nonsigular domination preserver and $T(A^t)=T(A)^t$ for $A\in {\Cal M}_{2,2}(\Cal S )$ if and only if $T$ is a term rank preserver on ${\Cal M(S)}$.

Keywords: linear preserver, domination, term rank

MSC numbers: 05C50, 15A04