A topological characterization of the goldman prime spectrum of a commutative ring

Abstract

A prime ideal p of a commutative ring R is said to be a Goldman ideal (or a G-ideal) if there exists a maximal ideal M of the polynomial ring R[X] such that p = M ∩ R. A topological space is said to be goldspectral if it is homeomorphic to the space Gold(R) of G-ideals of R (Gold(R) is considered as a subspace of the prime spectrum Spec(R) equipped with the Zariski topology). We give here a topological characterization of goldspectral spaces.

Keywords:

• G-ideal
• Zariski topology
• quasi-homeomorphism
• sober space

^∗Supported by the DGRST (E03/C15)

^∗Supported by the DGRST (E03/C15)

Notes

^∗Supported by the DGRST (E03/C15)