| 摘要: |
| 主要研究特殊Noether交换环弱CM环的性质.这类环包括Cohen-Macaulay环、优秀环和广义Cohen-Macaulay环,能够用局部上同调模来刻画.证明了如果R是弱CM环,则R的有限生成代数, 以及R关于理想I的I-adic完备化环均为弱CM环. |
| 关键词: 局部上同调模 一致局部上同调零化子 弱CM环 |
| DOI：10.3969/J.ISSN.1000-5137.2022.03.010 |
| 分类号:O192 |
| 基金项目:国家自然科学基金(11971317,11471083) |
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| On the properties of weak CM rings |
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XUE Wensi, ZHOU Caijun
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College of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology modules. We will prove that if R is a weak CM ring, then every finitely generated algebra of R and the I-adic complete ring of R with respect to any ideal I of R are still weak CM ring. |
| Key words: local cohomology uniform annihilator of local cohomology weak CM ring |
