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Matematicheskie Zametki, 2015, Volume 97, Issue 1, Pages 58–66
DOI: https://doi.org/10.4213/mzm10573
(Mi mzm10573)
 

This article is cited in 1 scientific paper (total in 1 paper)

$n$-Copure Projective Modules

Zenghui Gao

Chengdu University of Information Technology, China
Full-text PDF (477 kB) Citations (1)
References:
Abstract: Let $R$ be a ring, $n$ a fixed nonnegative integer and $\mathcal{F}_n$ the class of all left $R$-modules of flat dimension at most $n$. A left $R$-module $M$ is called $n$-copure projective if $\operatorname{Ext}_R^1(M,F)=0$ for any $F\in \mathcal{F}_n$. Some examples are given to show that $n$-copure projective modules need not be $m$-copure projective whenever $m>n$. Then we characterize the well-known QF rings and IF rings in terms of $n$-copure projective modules. Finally, we prove that a ring $R$ is relative left hereditary if and only if every submodule of a projective (or free) left $R$-module is $n$-copure projective if and only if $\operatorname{id}_R(N)\leqslant 1$ for every left $R$-module $N$ with $N\in \mathcal{F}_n$.
Keywords: $n$-copure projective module, strongly copure injective module, (relative) hereditary ring, QF ring, copure flat module.
Funding agency Grant number
National Natural Science Foundation of China 11301042
11171240
11226057
Chengdu University of Information Technology J201217
This work was supported in part by NSFC (grants nos. 11301042 and 11171240), by the Scientific Research Foundation of CUIT (grant no. J201217), and by NSFC (Tianyuan Fund for Mathematics) (grant no. 11226057).
Received: 15.12.2012
Revised: 14.05.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 1, Pages 50–56
DOI: https://doi.org/10.1134/S000143461501006X
Bibliographic databases:
Document Type: Article
UDC: 512.553
Language: Russian
Citation: Zenghui Gao, “$n$-Copure Projective Modules”, Mat. Zametki, 97:1 (2015), 58–66; Math. Notes, 97:1 (2015), 50–56
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v97/i1/p58
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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