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This article is cited in 1 scientific paper (total in 1 paper)
$n$-Copure Projective Modules
Zenghui Gao Chengdu University of Information Technology, China
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.
Received: 15.12.2012 Revised: 14.05.2014
Citation:
Zenghui Gao, “$n$-Copure Projective Modules”, Mat. Zametki, 97:1 (2015), 58–66; Math. Notes, 97:1 (2015), 50–56
Linking options:
https://www.mathnet.ru/eng/mzm10573https://doi.org/10.4213/mzm10573 https://www.mathnet.ru/eng/mzm/v97/i1/p58
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Abstract page: | 387 | Full-text PDF : | 174 | References: | 59 | First page: | 17 |
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