Abstract
Let R be a commutative ring with identity. We denote by Div(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 Div(R) of Spec(R) endowed with the Zariski topology, for some ring R. A divspectral set is a poset which is order isomorphic to (Div(R), ⊆), for some ring R. The main purpose of this paper is to provide some topological (resp., algebraic) characterizations of of divspectral spaces (resp., sets).
| Original language | English |
|---|---|
| Pages (from-to) | 453-467 |
| Number of pages | 15 |
| Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin |
| Volume | 26 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 Belgian Mathematical Society. All rights reserved.
Keywords
- Divided domains
- G-ideals
- Prime spectrum
- Valuation domains
- Zariski topology
ASJC Scopus subject areas
- General Mathematics
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