Strongly 0-Dimensional Rings

Jayaram C., Oral K. H., TEKİR Ü.

COMMUNICATIONS IN ALGEBRA, vol.41, no.6, pp.2026-2032, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2013
  • Doi Number: 10.1080/00927872.2011.618857
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2026-2032
  • Keywords: Compactly packed rings, Regular rings, Q-rings, Strongly prime ideals, Strongly 0-dimensional rings, Primary 13A15, Secondary 13A99, COMMUTATIVE RINGS, PRIME IDEALS, PROPERTY
  • Marmara University Affiliated: Yes

Abstract

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.