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 is finitely generated, then the R-module is faithful, i.e., . This result provides a partially affirmative answer to Lynch’s conjecture in [Citation10]. Moreover, in this paper we construct a counterexample to this conjecture.
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.