$k$-spaces of non-domain-valued geometric points
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912052313849856 |
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| author | Goswami, Amartya |
| author_facet | Goswami, Amartya |
| contents | The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the corresponding Zariski space. We prove that a $k$-space is $T_{\scriptscriptstyle 0}$, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such $k$-spaces. We conclude with a question about construction of a sheaf of $k$-spaces similar to affine schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01081 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $k$-spaces of non-domain-valued geometric points Goswami, Amartya Algebraic Geometry 14A20, 14A99, 16D25 The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the corresponding Zariski space. We prove that a $k$-space is $T_{\scriptscriptstyle 0}$, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such $k$-spaces. We conclude with a question about construction of a sheaf of $k$-spaces similar to affine schemes. |
| title | $k$-spaces of non-domain-valued geometric points |
| topic | Algebraic Geometry 14A20, 14A99, 16D25 |
| url | https://arxiv.org/abs/2302.01081 |