标题： 局部上同调模在局部化和完备化下的零化子 显示英文标题

标题： Annihilator of local cohomology modules under localization and completion

摘要： 设$(R, \frak m)$是一个诺特局部环。 本文研究了局部上同调模$H^i_{\frak m}(M)$的零化子与基环$R$的结构之间的关系，其中 $i$是非负整数，而$R$-模$M$是有限生成的。 首先，通过局部化和完备化下最高局部上同调模的零化子的相容性，分别表征了局部环的链性和无混性。 其次，给出了局部环成为 Cohen-Macaulay 局部环商的必要且充分条件，这些条件是通过局部化和完备化下所有局部上同调模的零化子来表述的。 显示英文摘要

摘要： Let $(R, \frak m)$ be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules $H^i_{\frak m}(M)$ in the relation with the structure of the base ring $R$, for non negative integers $i$ and finitely generated $R$-modules $M$. Firstly, the catenarity and the unmixedness of local rings are characterized via the compatibility of annihilator of top local cohomology modules under localization and completion, respectively. Secondly, some necessary and sufficient conditions for a local ring being a quotient of a Cohen-Macaulay local ring are given in term of the annihilator of all local cohomology modules under localization and completion.