C(\mathcal{X^{}})$-Cover and $C(\mathcal{X^{}})$-Envelope
Let $R$ be any associative ring with unity and $\mathcal{X}$ be a class of $R$-modules of closed under direct sum (and summands) and with extension closed. We prove that every complex has an $C(\mathcal{X^{*}})$-cover ($C(\mathcal{X^{*}})$-envelope) if every module has an $\mathcal{X}$-cover ($\math...
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| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
11.03.2011
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Let $R$ be any associative ring with unity and $\mathcal{X}$ be a class of
$R$-modules of closed under direct sum (and summands) and with extension
closed. We prove that every complex has an $C(\mathcal{X^{*}})$-cover
($C(\mathcal{X^{*}})$-envelope) if every module has an $\mathcal{X}$-cover
($\mathcal{X}$-envelope) where $C(\mathcal{X^{*}})$ is the class of complexes
of modules in $\mathcal{X}$ such that it is closed under direct and inverse
limit. |
|---|---|
| DOI: | 10.48550/arxiv.1103.2200 |