| Title:
|
Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings (English) |
| Author:
|
Bhat, Vijay Kumar |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
1049-1056 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a ring. We recall that $R$ is called a near pseudo-valuation ring if every minimal prime ideal of $R$ is strongly prime. Let now $\sigma $ be an automorphism of $R$ and $\delta $ a $\sigma $-derivation of $R$. Then $R$ is said to be an almost $\delta $-divided ring if every minimal prime ideal of $R$ is $\delta $-divided. Let $R$ be a Noetherian ring which is also an algebra over $\mathbb {Q}$ ($\mathbb {Q}$ is the field of rational numbers). Let $\sigma $ be an automorphism of $R$ such that $R$ is a $\sigma (*)$-ring and $\delta $ a $\sigma $-derivation of $R$ such that $\sigma (\delta (a)) = \delta (\sigma (a))$ for all $a \in R$. Further, if for any strongly prime ideal $U$ of $R$ with $\sigma (U) = U$ and $\delta (U)\subseteq \delta $, $U[x; \sigma , \delta ]$ is a strongly prime ideal of $R[x; \sigma , \delta ]$, then we prove the following: (1) $R$ is a near pseudo valuation ring if and only if the Ore extension $R[x; \sigma ,\delta ]$ is a near pseudo valuation ring. (2) $R$ is an almost $\delta $-divided ring if and only if $R[x;\sigma ,\delta ]$ is an almost $\delta $-divided ring. (English) |
| Keyword:
|
Ore extension |
| Keyword:
|
automorphism |
| Keyword:
|
derivation |
| Keyword:
|
minimal prime |
| Keyword:
|
pseudo-valuation ring |
| Keyword:
|
near pseudo-valuation ring |
| MSC:
|
16N40 |
| MSC:
|
16P40 |
| MSC:
|
16S36 |
| idZBL:
|
Zbl 1299.16020 |
| idMR:
|
MR3165514 |
| DOI:
|
10.1007/s10587-013-0071-8 |
| . |
| Date available:
|
2014-01-28T14:16:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143616 |
| . |
| Reference:
|
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