Abstract
Let $R$ be a commutative ring with identity. We denote by $\mathcal{D}\mathrm{iv}(R)$ the divided spectrum of $R$ (the set of all divided prime ideals of $R$). By a divspectral space, we mean a topological space homeomorphic with the subspace $\mathcal{D}\mathrm{iv}(R)$ of $\mathrm{Spec}(R)$ endowed with the Zariski topology, for some ring $R$. A divspectral set is a poset which is order isomorphic to $(\mathcal{D}\mathrm{iv}(R),\subseteq)$, for some ring $R$. The main purpose of this paper is to provide some topological (resp., algebraic) characterizations of of divspectral spaces (resp., sets).
Citation
Othman Echi. Adel Khalfallah. "Order theoretic and topological Characterizations of the Divided Spectrum of a Ring." Bull. Belg. Math. Soc. Simon Stevin 26 (3) 453 - 467, september 2019. https://doi.org/10.36045/bbms/1568685658
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