Geodesic
Monotone matrix maps and Skolem--Noether theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 46-49

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Monotone matrix maps induced by a group inverse are considered. The characterization is given in additive and continious cases. The ring version of Skolem–Noether theorem is obtained. A series of examples of nonlinear monotone maps are presented. 
@article{VMUMM_2012_5_a8,
     author = {M. A. Efimov},
     title = {Monotone matrix maps and {Skolem--Noether} theorem},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--49},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a8/}
}
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M. A. Efimov. Monotone matrix maps and Skolem--Noether theorem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 46-49. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a8/