COMPACTNESS OF A SUBSPACE OF THE ZARISKI TOPOLOGY ON SPEC(D)

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 3,  2011, pp.419-424
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.3.419
Title & Authors
COMPACTNESS OF A SUBSPACE OF THE ZARISKI TOPOLOGY ON SPEC(D)
Chang, Gyu-Whan;

Abstract
Let D be an integral domain, Spec(D) the set of prime ideals of D, and X a subspace of the Zariski topology on Spec(D). We show that X is compact if and only if given any ideal I of D with $\small{I{\nsubseteq}P}$ for all $\small{P{\in}X}$, there exists a finitely generated idea $\small{J{\subseteq}I}$ such that $\small{J{\nsubseteq}P}$ for all $\small{P{\in}X}$. We also prove that if D
Keywords
Zariski topology;subspace topology;compactness;* $\small{_f}$-Max(D);$\small{\mathcal{P}}$(D);
Language
English
Cited by
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