Rings with Property (A) and their extensions

By C. Hong, Nam Kyun Kim, Yang Lee, Sungju Ryu. 2007

47 citations recorded by the source corpus.

Abstract A commutative ring R has Property (A) if every finitely generated ideal of R consisting entirely of zero-divisors has a nonzero annihilator. We continue in this paper the study of rings with Property (A). We extend Property (A) to noncommutative rings, and study such rings. Moreover, we study several extensions of rings with Property (A) including matrix rings, polynomial rings, power series rings and classical quotient rings. Finally, we characterize when the space of minimal prime ideals of rings with Property (A) is compact.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/491eb78fbba28a8d07b9bf1c87a030cdcd12fad1