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Keywords:
zero-dimensional subring; filter; $\mathcal {F}$-topology; countably compact
zero-dimensional subring; filter; $\mathcal {F}$-topology; countably compact
Summary:
We investigate the relationship between the space $\mathcal {Z}(R,T)$, defined as the largest closed subset of a ring $T$ with respect to a countable topology, and the classical prime spectrum ${\rm Spect}(R)$ of a subring $R$. We explore the topological properties of $\mathcal {Z}(R,T)$ and establish connections with ${\rm Spect}(R)$ under certain conditions.
References:
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