On a particular subspace of homogeneous preserving star operations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916414381621248 |
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| author | Sahandi, Parviz |
| author_facet | Sahandi, Parviz |
| contents | Let $Γ$ be a torsionless commutative cancellative monoid, $R=\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded integral domain. In this note we show that each homogeneous star operation $\star:\mathbf{HF}(R)\to\mathbf{HF}(R)$ of $R$, is the restriction of a (classical) star operation $e(\star):F(R)\to F(R)$ of $R$. We also show that the set $HStar_f(R)$ of homogeneous star operations of finite type on $R$, endowed with the Zariski topology, is a spectral space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a particular subspace of homogeneous preserving star operations Sahandi, Parviz Commutative Algebra Let $Γ$ be a torsionless commutative cancellative monoid, $R=\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded integral domain. In this note we show that each homogeneous star operation $\star:\mathbf{HF}(R)\to\mathbf{HF}(R)$ of $R$, is the restriction of a (classical) star operation $e(\star):F(R)\to F(R)$ of $R$. We also show that the set $HStar_f(R)$ of homogeneous star operations of finite type on $R$, endowed with the Zariski topology, is a spectral space. |
| title | On a particular subspace of homogeneous preserving star operations |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2409.19602 |