Zariski subspace topologies on ideals

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ÖNEŞ O., ALKAN M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.48, sa.6, ss.1667-1674, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15672/hjms.2018.597
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1667-1674
  • Anahtar Kelimeler: prime ideal, radical ideal, Zariski topology, PRIME SPECTRUM, MODULE
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.