| 广义局部上同调模相伴素理想之集的有限性和Ext－模的弱拉斯克性 |
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| 引用本文： | 王晴.广义局部上同调模相伴素理想之集的有限性和Ext－模的弱拉斯克性[J].苏州大学学报(医学版),2009,25(3):19-22. |
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| 作者姓名： | 王晴 |
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| 作者单位： | 苏州大学,数学科学学院,江苏,苏州,215006 |
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| 摘 要： | 设R是含幺交换的Noether环，I是R的真理想，M，N是R-模．主要研究了广义局部上同调模H1（M,N）（ i≥0）相伴素理想之集的有限性和Ext-模的弱拉斯克性．用归纳法证明了：若M，N是有限生成模，i∈N0．若对 j〈i，有H1^j（M，N）为弱拉斯克模，则Ass（H1^i（M，N））是有限集．并给出了关于Ext-模的弱拉斯克性的几个等价条件．
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| 关 键 词： | 弱拉斯克 相伴素理想 广义局部上同调模 Ext-模 |
The finiteness for associated primes of the generalized local cohomology modules and the weakly Laskerian properties of some Ext-modules |
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| Wang Qing.The finiteness for associated primes of the generalized local cohomology modules and the weakly Laskerian properties of some Ext-modules[J].Journal of Suzhou University(Natural Science),2009,25(3):19-22. |
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| Authors: | Wang Qing |
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| Institution: | School of Mathematic Science;Suzhou Univ.;Suzhou 215006;China |
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| Abstract: | Let R be a commutative noetherian ring with identity, I a proper ideal of R and M, N are both R-modules. We mainly study the finiteness for associated primes of the generalized local cohomology modules H1^i （M, N） （ i≥0） and the weakly Laskerian properties of some Ext-modules. We use induction to prove：If M,N are both finitely generated R-modules,/E No such that H1^j（M,N） is weakly L,askerian（ j 〈 i） ,then the set Ass（H1^i（M,N） ） is finite. Also we give some equivalent conditions of the weakly Laskerian properties of some Ext-modules. |
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| Keywords: | weakly Laskerian associated primes generalized local cohomology module Ext-module |
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