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.

中文翻译：

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关于Chern系数和Cohen-Macaulay环的注释

在本文中，我们研究了可归约性指数与主要理想的Chern系数之间的关系。作为应用，我们针对Nohenian局部环中的某些参数理想，根据其类型，不可约多重性和Chern系数对Cohen-Macaulay环进行了表征。