AI 中文总结
该研究探讨Cohen-Macaulay局部环中Ulrich模的基本性质，证明其可分解，并据此讨论具有极小重数环的若干刻画及作为模为Ulrich的理想的性质。
AI 中文摘要
本文研究Ulrich模的一些基本性质，证明Cohen-Macaulay局部环中的Ulrich模是可分解的。作为结果，本文讨论了为具有极小重数的环所证明的一些刻画，以及作为模为Ulrich的理想的一些性质。
英文摘要
Some basic properties of Ulrich modules are studied and it is proved that Ulrich modules in Cohen-Macaulay local rings are decomposable. As a result, some characterizations proved for rings having minimal multiplicity, and some properties for ideals which are Ulrich as module is discussed.
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