Notes on the zero-divisor graph and annihilating-ideal graph of a reduced ring

We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾...

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Bibliographic Details
Main Author: Badie Mehdi
Format: Article
Language:English
Published: Sciendo 2021-06-01
Series:Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Subjects:
Online Access:https://doi.org/10.2478/auom-2021-0018