| Title:
|
On strongly affine extensions of commutative rings (English) |
| Author:
|
Zeidi, Nabil |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
251-260 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ring extension $R\subseteq S$ is said to be strongly affine if each $R$-subalgebra of $S$ is a finite-type $R$-algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if $R$ is a quasi-local ring of finite dimension, then $R\subseteq S$ is integrally closed and strongly affine if and only if $R\subseteq S$ is a Prüfer extension (i.e. $(R,S)$ is a normal pair). As a consequence, the equivalence of strongly affine extensions, quasi-Prüfer extensions and INC-pairs is shown. Let $G$ be a subgroup of the automorphism group of $S$ such that $R$ is invariant under action by $G$. If $R\subseteq S$ is strongly affine, then $R^G\subseteq S^G$ is strongly affine under some conditions. (English) |
| Keyword:
|
strongly affine |
| Keyword:
|
Prüfer extension |
| Keyword:
|
finitely many intermediate algebras property extension |
| Keyword:
|
finite chain propery extension |
| Keyword:
|
normal pair |
| Keyword:
|
integrally closed pair |
| Keyword:
|
ring of invariants |
| MSC:
|
13A15 |
| MSC:
|
13A50 |
| MSC:
|
13B02 |
| MSC:
|
13E05 |
| idZBL:
|
07217132 |
| idMR:
|
MR4078357 |
| DOI:
|
10.21136/CMJ.2019.0240-18 |
| . |
| Date available:
|
2020-03-10T10:19:26Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148053 |
| . |
| Reference:
|
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