| Title:
|
P-injective group rings (English) |
| Author:
|
Shen, Liang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1103-1109 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ring $R$ is called right P-injective if every homomorphism from a principal right ideal of $R$ to $R_R$ can be extended to a homomorphism from $R_R$ to $R_R$. Let $R$ be a ring and $G$ a group. Based on a result of Nicholson and Yousif, we prove that the group ring ${\rm RG}$ is right P-injective if and only if (a) $R$ is right P-injective; (b) $G$ is locally finite; and (c) for any finite subgroup $H$ of $G$ and any principal right ideal $I$ of ${\rm RH}$, if $f\in {\rm Hom}_R(I_R, R_R)$, then there exists $g\in {\rm Hom}_R({\rm RH}_R, R_R)$ such that $g|_I=f$. Similarly, we also obtain equivalent characterizations of $n$-injective group rings and F-injective group rings. (English) |
| Keyword:
|
group ring |
| Keyword:
|
P-injective ring |
| Keyword:
|
$n$-injective ring |
| Keyword:
|
F-injective ring |
| MSC:
|
16D50 |
| MSC:
|
16S34 |
| idZBL:
|
07285982 |
| idMR:
|
MR4181799 |
| DOI:
|
10.21136/CMJ.2020.0159-19 |
| . |
| Date available:
|
2020-11-18T09:47:37Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148414 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Nicholson, W. K., Yousif, M. F.: Principally injective rings.J. Algebra 174 (1995), 77-93. Zbl 0839.16004, MR 1332860, 10.1006/jabr.1995.1117 |
| Reference:
|
[6] Nicholson, W. K., Yousif, M. F.: Quasi-Frobenius Rings.Cambridge Tracts in Mathematics 158, Cambridge University Press, Cambridge (2003). Zbl 1042.16009, MR 2003785, 10.1017/CBO9780511546525 |
| Reference:
|
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| . |
