Zariski subspace topologies on ideals


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ÖNEŞ O., ALKAN M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.6, pp.1667-1674, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.597
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1667-1674
  • Keywords: prime ideal, radical ideal, Zariski topology, PRIME SPECTRUM, MODULE
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we show how there are tight relationships between algebraic properties of a commutative ring R and topological properties of open subsets of Zariski topology on the prime spectrum of R. We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also give a characterization for the radical of an ideal in R by using topological properties.