k-spaces of non-domain-valued geometric points
Submitted: 2023-06-15
|Accepted: 2024-03-28
|Published: 2024-10-01
Copyright (c) 2024 Amartya Goswami
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
geometric point, connectedness, spectral space
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Abstract:
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 T0, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such k-spaces. We conclude with a question about the construction of a sheaf of k-spaces similar to affine schemes.
References:
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