Abstract
A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and Π-coherent rings with property (P).
Acknowledgments
The first author was partially supported by National Natural Science Foundation of China (Grant No. 10001017), Scientific Research Foundation for Returned Overseas Chinese Scholars (State Education Ministry) and Nanjing University Talent Development Foundation. The second author was partially supported by Guangxi Natural Science Foundation (Grant No. 0229021).