Arkiv för Matematik

Volume 58 (2020)

Number 1

A note on Chern coefficients and Cohen–Macaulay rings

Pages: 197 – 212



Nguyen Thi Thanh Tam (Hung Vuong University, Viet Tri, Phu Tho, Vietnam)

Hoang Le Truong (Mathematik und Informatik, Universität des Saarlandes, Saarbrücken, Germany; Institute of Mathematics, VAST, Hanoi, Vietnam; and Thang Long Institute of Mathematics and Applied Sciences, Hanoi, Vietnam)


In this paper, we investigate the relationship between the index of reducibility and Chern coefficients for primary ideals. As an application, we give characterizations of a Cohen–Macaulay ring in terms of its type, irreducible multiplicity, and Chern coefficients with respect to certain parameter ideals in Noetherian local rings.


index of reducibility, Cohen–Macaulay, irreducible multiplicity, Chern number, Hilbert coefficients

2010 Mathematics Subject Classification

13A15, 13D45, 13H10, 13H15

This work is partially supported by a fund of Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2017.14.

Received 14 January 2019

Received revised 30 August 2019

Accepted 20 September 2019

Published 21 July 2022