A topological version of Hilbert's Nullstellensatz

TL;DR

This paper establishes a topological framework connecting radical ideals of a ring with Zariski closed subspaces, showing both form spectral spaces and are homeomorphic.

Contribution

It introduces a topological perspective on radical ideals and Zariski closed subspaces, revealing their spectral space structure and homeomorphism.

Findings

Space of radical ideals is spectral

Homeomorphism with Zariski closed subspaces

Provides a new topological characterization of algebraic structures

Abstract

We prove that the space of radical ideals of a ring $R$, endowed with the hull-kernel topology, is a spectral space, and that it is canonically homeomorphic to the space of the nonempty Zariski closed subspaces of Spec$(R)$, endowed with a Zariski-like topology.