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Cohen-Macaulay rings and modules play a central role in modern commutative algebra. This class of modules is distinguished in many ways, which will become apparent in this chapter. Polynomial rings over a field, complete intersection rings and Artinian rings are examples of Cohen-Macaulay rings. We review the main properties of Cohen-Macaulay modules and the canonical module of a finitely generated graded K-algebras.

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Cohen-Macaulay Modules and the Canonical Module

  • 章节

  • 发表日期：

    2026年

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  • Jürgen Herzog,
  • Somayeh Moradi,
  • Masoomeh Rahimbeigi

摘要

Cohen-Macaulay rings and modules play a central role in modern commutative algebra. This class of modules is distinguished in many ways, which will become apparent in this chapter. Polynomial rings over a field, complete intersection rings and Artinian rings are examples of Cohen-Macaulay rings. We review the main properties of Cohen-Macaulay modules and the canonical module of a finitely generated graded K-algebras.