A Zariski-like topology on the ideal spectrum of a ring

Amartya Goswami

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arXiv · 2106.11363

A Zariski-like topology on the ideal spectrum of a ring

Amartya Goswami

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Abstract

The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducible closed subset has a unique generic point. Furthermore, this space is weaker than a spectral space and if the ring has a non-trivial idempotent element then the space has a closed disconnected subspace.

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Amartya Goswami. 2021-06-21. A Zariski-like topology on the ideal spectrum of a ring. https://arxiv.org/abs/2106.11363

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