The class of Gorenstein injective modules is covering if and only if it is closed under direct limits
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929501086154752 |
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| author | Iacob, Alina |
| author_facet | Iacob, Alina |
| contents | We prove that the class of Gorenstein injective modules, $\mathcal{GI}$, is special precovering if and only if it is covering if and only if it is closed under direct limits. This adds to the list of examples that support Enochs' conjecture:\\ "Every covering class of modules is closed under direct limits".\\ We also give a characterization of the rings for which $\mathcal{GI}$ is covering: the class of Gorenstein injective left $R$-modules is covering if and only if $R$ is left noetherian, and such that character modules of Gorenstein injective left $R$ modules are Gorenstein flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The class of Gorenstein injective modules is covering if and only if it is closed under direct limits Iacob, Alina Commutative Algebra We prove that the class of Gorenstein injective modules, $\mathcal{GI}$, is special precovering if and only if it is covering if and only if it is closed under direct limits. This adds to the list of examples that support Enochs' conjecture:\\ "Every covering class of modules is closed under direct limits".\\ We also give a characterization of the rings for which $\mathcal{GI}$ is covering: the class of Gorenstein injective left $R$-modules is covering if and only if $R$ is left noetherian, and such that character modules of Gorenstein injective left $R$ modules are Gorenstein flat. |
| title | The class of Gorenstein injective modules is covering if and only if it is closed under direct limits |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2403.02493 |