Geodesic
The group of commutativity preserving maps on strictly upper triangular matrices
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 335-350.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $\mathcal {N}=N_n(R)$ be the algebra of all $n\times n$ strictly upper triangular matrices over a unital commutative ring $R$. A map $\varphi $ on $\mathcal {N}$ is called preserving commutativity in both directions if $xy=yx\Leftrightarrow \varphi (x)\varphi (y)=\varphi (y)\varphi (x)$. In this paper, we prove that each invertible linear map on $\mathcal {N}$ preserving commutativity in both directions is exactly a quasi-automorphism of $\mathcal {N}$, and a quasi-automorphism of $\mathcal {N}$ can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.
DOI : 10.1007/s10587-014-0105-x
Classification : 13C10, 15A04, 15A27, 15A99, 17C30
Keywords: commutativity preserving map; automorphism; commutative ring 
@article{10_1007_s10587_014_0105_x,
     author = {Wang, Dengyin and Zhu, Min and Rou, Jianling},
     title = {The group of commutativity preserving maps on strictly upper triangular matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {335--350},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {2014},
     doi = {10.1007/s10587-014-0105-x},
     mrnumber = {3277740},
     zbl = {06391498},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0105-x/}
}
TY  - JOUR
AU  - Wang, Dengyin
AU  - Zhu, Min
AU  - Rou, Jianling
TI  - The group of commutativity preserving maps on strictly upper triangular matrices
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 335
EP  - 350
VL  - 64
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0105-x/
DO  - 10.1007/s10587-014-0105-x
LA  - en
ID  - 10_1007_s10587_014_0105_x
ER  - 
%0 Journal Article
%A Wang, Dengyin
%A Zhu, Min
%A Rou, Jianling
%T The group of commutativity preserving maps on strictly upper triangular matrices
%J Czechoslovak Mathematical Journal
%D 2014
%P 335-350
%V 64
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0105-x/
%R 10.1007/s10587-014-0105-x
%G en
%F 10_1007_s10587_014_0105_x
Wang, Dengyin; Zhu, Min; Rou, Jianling. The group of commutativity preserving maps on strictly upper triangular matrices. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 335-350. doi : 10.1007/s10587-014-0105-x. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0105-x/

Cité par Sources :