首页 | 本学科首页   官方微博 | 高级检索  
     


Asymptotic behaviour of certain sets of prime ideals
Authors:Alan K. Kingsbury   Rodney Y. Sharp
Affiliation:Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, United Kingdom ; Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, United Kingdom
Abstract:Let $I_{1}, ldots ,I_{g}$ be ideals of the commutative ring $R$, let $M$ be a Noetherian $R$-module and let $N$ be a submodule of $M$; also let $A$ be an Artinian $R$-module and let $B$ be a submodule of $A$. It is shown that, whenever $left (a_{m}left (1right ),ldots ,a_{m}left (gright )right )_{min mathbb {N}}$ is a sequence of $g$-tuples of non-negative integers which is non-decreasing in the sense that $a_{i}left (jright )leq a_{i+1}left (jright )$ for all $j=1,ldots ,g$ and all $iin mathbb {N}$, then Ass$_{R}left (M/ I_{1}^{a_{n}left (1right )}ldots I_{g}^{a_{n}left (gright )}Nright )$ is independent of $n$ for all large $n$, and also Att$_{R}left (B:_{A}I_{1}^{a_{n}left (1right )}ldots I_{g}^{a_{n}left (gright )}right )$ is independent of $n$ for all large $n$. These results are proved without any regularity conditions on the ideals $I_{1}, ldots ,I_{g}$, and so (a special case of) the first answers in the affirmative a question raised by S. McAdam.

Keywords:Associated prime ideal   attached prime ideal   Noetherian module   Artinian module   asymptotic prime divisors
点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
点击此处可从《Proceedings of the American Mathematical Society》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号