ABSTRACT
Let (R,𝔪) be a Cohen-Macaulay local ring of positive dimension d and infinite residue field. Let I be an 𝔪-primary ideal and J a minimal reduction of I. In this paper, we show that . This answer to a question that made by Rossi and Swanson in [Citation15, Question 4.6].
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Acknowledgments
This paper was done while I was visiting the University of Osnabruck. I would like to thank the Institute of Mathematics of the University of Osnabruck for hospitality. Also, I would like to express my deep gratitude to Professor Louis Ratliff and Professor Tony Puthenpurakal for valuable suggestions. Finally, I would like grateful to the referee for the careful reading of the manuscript and the helpful suggestions.