Geodesic
A note on Skolem-Noether algebras
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 137-154 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The paper was motivated by Kovacs' paper (1973), Isaacs' paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let $K$ be a unital commutative ring, not necessarily a field. Given a unital $K$-algebra $S$, where $K$ is contained in the center of $S$, $n\in \mathbb N$, the goal of this paper is to study the question: when can a homomorphism $\phi \colon {\rm M}_n(K)\to {\rm M}_n(S)$ be extended to an inner automorphism of ${\rm M}_n(S)$? As an application of main results presented in the paper, it is proved that if $S$ is a semilocal algebra with a central separable subalgebra $R$, then any homomorphism from $R$ into $S$ can be extended to an inner automorphism of $S$.
The paper was motivated by Kovacs' paper (1973), Isaacs' paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let $K$ be a unital commutative ring, not necessarily a field. Given a unital $K$-algebra $S$, where $K$ is contained in the center of $S$, $n\in \mathbb N$, the goal of this paper is to study the question: when can a homomorphism $\phi \colon {\rm M}_n(K)\to {\rm M}_n(S)$ be extended to an inner automorphism of ${\rm M}_n(S)$? As an application of main results presented in the paper, it is proved that if $S$ is a semilocal algebra with a central separable subalgebra $R$, then any homomorphism from $R$ into $S$ can be extended to an inner automorphism of $S$.
DOI : 10.21136/CMJ.2020.0215-19
Classification : 16K20, 16S50, 16W20
Keywords: Skolem-Noether algebra; (inner) automorphism; matrix algebra; central simple algebra; central separable algebra; semilocal ring; unique factorization domain (UFD); stably finite ring; Dedekind-finite ring 
@article{10_21136_CMJ_2020_0215_19,
     author = {Han, Juncheol and Lee, Tsiu-Kwen and Park, Sangwon},
     title = {A note on {Skolem-Noether} algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {137--154},
     year = {2021},
     volume = {71},
     number = {1},
     doi = {10.21136/CMJ.2020.0215-19},
     mrnumber = {4226474},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0215-19/}
}
TY  - JOUR
AU  - Han, Juncheol
AU  - Lee, Tsiu-Kwen
AU  - Park, Sangwon
TI  - A note on Skolem-Noether algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 137
EP  - 154
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0215-19/
DO  - 10.21136/CMJ.2020.0215-19
LA  - en
ID  - 10_21136_CMJ_2020_0215_19
ER  - 
%0 Journal Article
%A Han, Juncheol
%A Lee, Tsiu-Kwen
%A Park, Sangwon
%T A note on Skolem-Noether algebras
%J Czechoslovak Mathematical Journal
%D 2021
%P 137-154
%V 71
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0215-19/
%R 10.21136/CMJ.2020.0215-19
%G en
%F 10_21136_CMJ_2020_0215_19
Han, Juncheol; Lee, Tsiu-Kwen; Park, Sangwon. A note on Skolem-Noether algebras. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 137-154. doi: 10.21136/CMJ.2020.0215-19

Cité par Sources :