A characterization of monoid graded semihereditary rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918490561052672 |
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| author | Sahandi, Parviz Shirmohammadi, Nematollah |
| author_facet | Sahandi, Parviz Shirmohammadi, Nematollah |
| contents | Let $Γ$ be a cancellation monoid and $R=\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent and every graded submodule of a flat left $R$-module is flat. Hence it gives a new characterization of graded-Prüfer domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A characterization of monoid graded semihereditary rings Sahandi, Parviz Shirmohammadi, Nematollah Rings and Algebras Commutative Algebra 16W50, 16D40, 16E60, 13F05 Let $Γ$ be a cancellation monoid and $R=\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent and every graded submodule of a flat left $R$-module is flat. Hence it gives a new characterization of graded-Prüfer domains. |
| title | A characterization of monoid graded semihereditary rings |
| topic | Rings and Algebras Commutative Algebra 16W50, 16D40, 16E60, 13F05 |
| url | https://arxiv.org/abs/2605.08095 |