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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
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Category: math
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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
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Date available: 2020-11-18T09:47:37Z
Last updated: 2021-02-10
Stable URL: http://hdl.handle.net/10338.dmlcz/148414
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