Strongly 0-Dimensional Rings - TEKİR, ÜNSAL (TAYLOR & FRANCIS INC, 2013)
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.
Keywords: Compactly packed rings; Regular rings; Q-rings; Strongly prime ideals; Strongly 0-dimensional rings; Primary 13A15; Secondary 13A99; COMMUTATIVE RINGS; PRIME IDEALS; PROPERTY