Chern coefficients and Cohen-Macaulay rings

In this study, we investigate the relationship between the index of reducibility and Chern coefficients for primary ideals. Therefore, the main result of this study provides a characterization of a Cohen-Macaulay ring in terms of its index of reducibility, Cohen-Macaulay type, and the Chern coefficients for parameter ideals. As corollaries to the main theorem, we obtain characterizations of a Gorenstein ring in terms of its Chern coefficients for parameter ideals.