(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 $\overset \left\{\sharp \right\}\left\{\leq \right\}$- and $\overset \left\{\mathrm \left\{cn\right\}\right\}\left\{\leq \right\}$-orders and build some examples of nonadditive monotone maps.

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