We introduce the notion of z-ideal, which arises in a natural way in the study of the rings of real-valued continuous functions and which can be generalized to arbitrary rings. We describe the properties of z-ideals and study the relationship with 0-ideals. Furthermore we prove that there is an interesting connection between the z-ideals of a ring and the prime spectrum of the maximal ring of quotients.
A subspace of Spec(A) and its connexions with the maximal ring of quotients
ARTICO, GIULIANO;MARCONI, UMBERTO;MORESCO, ROBERTO
1981
Abstract
We introduce the notion of z-ideal, which arises in a natural way in the study of the rings of real-valued continuous functions and which can be generalized to arbitrary rings. We describe the properties of z-ideals and study the relationship with 0-ideals. Furthermore we prove that there is an interesting connection between the z-ideals of a ring and the prime spectrum of the maximal ring of quotients.
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