Let be a -dimensional Cohen–Macaulay local ring, be an -primary ideal of and let be a minimal reduction of . We show that if, for or , and , then . Moreover, we prove that if , or if and is integrally closed, then , where the integers are the Hilbert coefficients of . In addition, if is a minimal reduction of then we prove that the reduction number is independent of .
"On the Hilbert coefficients, depth of associated graded rings and reduction numbers." J. Commut. Algebra 13 (1) 103 - 115, Spring 2021. https://doi.org/10.1216/jca.2021.13.103