FPM 2011/2012, vol. 17, no. 6, pp. 23-40

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 6, PAGES 23-40

Additive matrix maps that are monotone with respect to the orders induced by group inverse

M. A. Efimov

Abstract

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We characterize additive maps on the matrix algebra over an arbitrary field with three or more elements that are monotone with respect to the $$ \overset {\sharp }{\leq }
$$ - and $$
\overset {\mathrm {cn}}{\leq } $$ -orders and build some examples of nonadditive monotone maps.

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