| Title:
|
A note on Skolem-Noether algebras (English) |
| Author:
|
Han, Juncheol |
| Author:
|
Lee, Tsiu-Kwen |
| Author:
|
Park, Sangwon |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
137-154 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $S$. (English) |
| Keyword:
|
Skolem-Noether algebra |
| Keyword:
|
(inner) automorphism |
| Keyword:
|
matrix algebra |
| Keyword:
|
central simple algebra |
| Keyword:
|
central separable algebra |
| Keyword:
|
semilocal ring |
| Keyword:
|
unique factorization domain (UFD) |
| Keyword:
|
stably finite ring |
| Keyword:
|
Dedekind-finite ring |
| MSC:
|
16K20 |
| MSC:
|
16S50 |
| MSC:
|
16W20 |
| idZBL:
|
07332709 |
| idMR:
|
MR4226474 |
| DOI:
|
10.21136/CMJ.2020.0215-19 |
| . |
| Date available:
|
2021-03-12T16:11:28Z |
| Last updated:
|
2023-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148732 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[11] Rowen, L.: Some results on the center of a ring with polynomial identity.Bull. Am. Math. Soc. 79 (1973), 219-223. Zbl 0252.16007, MR 0309996, 10.1090/S0002-9904-1973-13162-3 |
| Reference:
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| . |
