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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
To conclude, we give examples related to $B(Omega_2(R_m),t)$ for various rings R.
📌 3 Key Takeaways
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Objective & Hypothesis:Let R be the coordinate ring of an affine irreducible curve presented by $frac{k[x,y]}{(f)}$ and m a maximal ideal of R.
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Key Findings & Data:Let $Omega_2(R_m)$ be the universal module of second order derivations of $R_m$.
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Conclusion & Impact:To conclude, we give examples related to $B(Omega_2(R_m),t)$ for various rings R.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let R be the coordinate ring of an affine irreducible curve presented by $frac{k[x,y]}{(f)}$ and m a maximal ideal of R. Assume that $R_m$, the localization of R at m, is not a regular ring. Let $Omega_2(R_m)$ be the universal module of second order derivations of $R_m$. We show that, under certain conditions, $B(Omega_2(R_m), t)$, the Betti series of$Omega_2(R_m)$, is a rational function. To conclude, we give examples related to $B(Omega_2(R_m),t)$ for various rings R.
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Cite This Article
ERDOĞAN, A. (2022). Result on Betti series of the universal modules of second order derivations. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 3, 449–452. https://ajindex.com/articles/530563