$C(\mathcal{X^{*}})$-Cover and $C(\mathcal{X^{*}})$-Envelope

Details $C(\mathcal{X^{*}})$-Cover and $C(\mathcal{X^{*}})$-Envelope $C(\mathcal{X^{*}})$-Cover and $C(\mathcal{X^{*}})$-Envelope

2011-03-11

arxiv.org/abs/1103.2200v1

Mathematics

Rings and Algebras

Scientific paper

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.

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