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Original Articles

A note on Lynch’s conjecture

Pages 2738-2745 | Received 12 May 2016, Published online: 07 Oct 2016
 

ABSTRACT

Let R be a commutative Noetherian domain and let I be an ideal of R. In this paper it is shown that if cd(I,R) = t>0 and the R-module HomR(RI,HIt(R)) is finitely generated, then the R-module HIt(R) is faithful, i.e., AnnHIt(R)=0. This result provides a partially affirmative answer to Lynch’s conjecture in [Citation10]. Moreover, in this paper we construct a counterexample to this conjecture.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

The author would like to thank Professor Reza Naghipour for his careful reading of the first draft and many helpful suggestions. Also he would like to thank Mohaghegh Ardabili University for its financial support.

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