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Communications in Algebra Volume 31, 2003 - Issue 12
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Original Articles

Homological Characterizations of Rings with Property (P)

Zhaoyong Huang Department of Mathematics, Nanjing University, Nanjing, P.R. China; Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. ChinaCorrespondence[email protected]
&
Gaohua Tang Department of Mathematics, Guangxi Teachers' College, Nanning, P.R. China; Department of Mathematics, Guangxi Teachers' College, Nanning, 530001, P.R. ChinaCorrespondence[email protected]
Pages 6149-6159 | Received 01 Jul 2002, Published online: 01 Feb 2007
 
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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).

2000 Mathematics Subject Classification:

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).

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