Strongly 0-Dimensional Rings

Jayaram C., Oral K. H., TEKİR Ü.

COMMUNICATIONS IN ALGEBRA, cilt.41, sa.6, ss.2026-2032, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 6
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/00927872.2011.618857
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2026-2032
  • Anahtar Kelimeler: Compactly packed rings, Regular rings, Q-rings, Strongly prime ideals, Strongly 0-dimensional rings, Primary 13A15, Secondary 13A99, COMMUTATIVE RINGS, PRIME IDEALS, PROPERTY
  • Marmara Üniversitesi Adresli: Evet

Özet

A commutative ring R with identity is called a strongly 0-dimensional ring if whenever a prime ideal P of R, contains the intersection of any family of ideals, then P contains one of the ideals of the family. In this article, we establish several equivalent conditions for a commutative ring R with identity to be a strongly 0-dimensional ring. We also characterize Artinian rings in terms of strongly 0-dimensional rings.