We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically Gorenstein. We compare these modules to Cohen–Macaulay modules over the endomorphism ring of the maximal ideal. After this comparison, we give several characterizations of almost Gorenstein rings in terms of syzygies of Cohen–Macaulay modules.

中文翻译：

---

一维Cohen-Macaulay局部环上的Cohen-Macaulay模块的Syzygie

我们研究在一维Cohen-Macaulay局部环上的（最大）Cohen-Macaulay模块的合音。我们假设环一般是戈伦斯坦。我们将这些模块与最大理想内环上的Cohen–Macaulay模块进行比较。经过比较之后，我们根据Cohen-Macaulay模块的同构关系给出了几乎Gorenstein环的几个特征。