Geodesic
Monotone matrix maps and Skolem–Noether theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 46-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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{\textendash}Noether} theorem},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--49},
     year = {2012},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a8/}
}
TY  - JOUR
AU  - M. A. Efimov
TI  - Monotone matrix maps and Skolem–Noether theorem
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 46
EP  - 49
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a8/
LA  - ru
ID  - VMUMM_2012_5_a8
ER  - 
%0 Journal Article
%A M. A. Efimov
%T Monotone matrix maps and Skolem–Noether theorem
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 46-49
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a8/
%G ru
%F VMUMM_2012_5_a8
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/

[1] De Pillis J., “Linear transformations which preserve Hermitian and positive semidefinite operators”, Pacif. J. Math., 23 (1967), 129–137 | DOI | MR

[2] Guterman A., “Linear preservers for Drazin star partial order”, Communs Algebra, 29:9 (2001), 3905–3917 | DOI | MR

[3] Guterman A., “Linear preservers for matrix inequalities and partial orderings”, Linear Algebra and Its Appl., 331:1–3 (2001), 75–87 | DOI | MR

[4] Mikhalev A.V., “Isomorphisms and anti-isomorphisms of endomorphism rings of modules”, First Int. Tainan–Moscow Algebra Workshop, Walter de Gruyter $\$ Co, Berlin–N.Y., 1995, 69–122 | MR

[5] Pierce S., Lim M.H., Loew R., Li C.K., Tsing N.K., McDonald B., Beasley L., “A survey of linear preserver problems”, Linear and Multilinear Algebra, 33 (1992), 1–119 | DOI | MR

[6] Baksalary J.K., Pukelsheim F., Styan G.P.H., “Some properties of matrix partial orderings”, Linear Algebra and Its Appl., 119 (1989), 57–85 | DOI | MR

[7] Ovchinnikov P.G., “Automorphisms of the poset of skew projections”, J. Funct. Anal., 115 (1993), 184–189 | DOI | MR

[8] Šemrl P., “Order-preserving maps on the poset of idempotent matrices”, Acta sci. math. (Szeged), 69 (2003), 481—490 | MR

[9] Legiša P., “Automorphisms of $M_n$, partially ordered by rank subtractivity ordering”, Linear Algebra and Its Appl., 389 (2004), 147–158 | DOI | MR

[10] Mitra S.K., “A new class of $g$-inverse of square matrices”, Sankhya. Ser. A, 30 (1963), 323–330 | MR

[11] Mitra S.K., “On group inverses and the sharp order”, Linear Algebra and Its Appl., 92 (1987), 17–37 | DOI | MR

[12] Ben-Israel A., Greville T., Generalized Inverses: Theory and Applications, John Wiley and Sons, N.Y., 1974 | MR

[13] Rao C.R., Mitra S.K., Generalized Inverse of Matrices and its Applications, Wiley, N.Y., 1971 | MR

[14] Hartwig R. E., “How to partially order regular elements”, Math. Japonica, 25:1 (1980), 1–13 | MR

[15] Nambooripad K. S. S., “The natural partial order on a regular semigroup”, Proc. Edinburgh Math. Soc., 23 (1980), 249–260 | DOI | MR

[16] Hartwig R. E., Mitra S. K., “Partial orders based on outer inverses”, Linear Algebra and Its Appl., 176 (1992), 3–20 | DOI | MR

[17] Bogdanov I.I., Guterman A.E., “Monotonnye otobrazheniya matrits, zadannye gruppovoi obratnoi, i odnovremennaya diagonalizuemost”, Matem. sb., 198:1 (2007), 3–20 | DOI | MR

[18] Efimov M.A., “Lineinye otobrazheniya matrits, monotonnye otnositelno $\overset\sharp\leq $, $\overset{\mathrm{cn}}\leq $-poryadkov”, Fund. i prikl. matem., 13:4 (2007), 53–66

[19] Pirs R., Assotsiativnye algebry, Mir, M., 1986 | MR