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

Location: http://mech.math.msu.su/~fpm/eng/k1112/k116/k11602h.htm

Last modified: November 21, 2012