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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
It is shown that, whenever I is principal, then for each integer $i$ the set of associated prime ideals $Ass_R Ext^i_R(R/I^n , M)$, $n = 1, 2, . . . ,$ becomes independent of $n$, for large $n$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let R be a commutative Noetherian ring, I an ideal of R and M a finitely generated R-module.
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Key Findings & Data:Let R be a commutative Noetherian ring, I an ideal of R and M a finitely generated R-module.
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Conclusion & Impact:It is shown that, whenever I is principal, then for each integer $i$ the set of associated prime ideals $Ass_R Ext^i_R(R/I^n , M)$, $n = 1, 2, . . . ,$ becomes independent of $n$, for large $n$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Artinian module · Associated prime · Depth
Abstract
Let R be a commutative Noetherian ring, I an ideal of R and M a finitely generated R-module. It is shown that, whenever I is principal, then for each integer $i$ the set of associated prime ideals $Ass_R Ext^i_R(R/I^n , M)$, $n = 1, 2, . . . ,$ becomes independent of $n$, for large $n$.
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Cite This Article
Bahmanpour, K., Naghipour, R., Sehatkhah, M. (2016). Asymptotic behavior of associated primes of certain ext modules. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 5. https://ajindex.com/articles/1403091