The space of homogeneous preserving semistar operations on graded domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916417761181696 |
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| author | Sahandi, Parviz |
| author_facet | Sahandi, Parviz |
| contents | Let $R=\bigoplus_{α\inΓ}R_α$ be a graded integral domain. In this paper we study the space of homogeneous preserving semistar operations on $R$. We show if $\star$ is a homogeneous preserving semistar operation on $R$, then $\star_a$ is also homogeneous preserving. Let $KR(R,b)$ be the homogeneous Kronecker function ring of $R$ with respect to the $b$-operation. It is shown that the set of valuation overrings of $KR(R,b)$, endowed with the Zariski topology, is homeomorphism to $Zar_h(R)$, the set of gr-valuation overrings of $R$, endowed with the Zariski topology. We also show that the set $SStar_{f,hp}(R)$ of finite type, homogeneous preserving semistar operations on $R$, endowed with the Zariski topology, is a spectral space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The space of homogeneous preserving semistar operations on graded domains Sahandi, Parviz Commutative Algebra Let $R=\bigoplus_{α\inΓ}R_α$ be a graded integral domain. In this paper we study the space of homogeneous preserving semistar operations on $R$. We show if $\star$ is a homogeneous preserving semistar operation on $R$, then $\star_a$ is also homogeneous preserving. Let $KR(R,b)$ be the homogeneous Kronecker function ring of $R$ with respect to the $b$-operation. It is shown that the set of valuation overrings of $KR(R,b)$, endowed with the Zariski topology, is homeomorphism to $Zar_h(R)$, the set of gr-valuation overrings of $R$, endowed with the Zariski topology. We also show that the set $SStar_{f,hp}(R)$ of finite type, homogeneous preserving semistar operations on $R$, endowed with the Zariski topology, is a spectral space. |
| title | The space of homogeneous preserving semistar operations on graded domains |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2410.00437 |