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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 1

On Betti series of the universal modules of second order derivations of k[x1,x2,...,xs] (f)

Ali ERDOGAN
Halise Melis AKCIN TEKIN
Pages
25–28
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We proved that the Betti series of Ω2(Rm), where Ω2(Rm) denotes the universal module of second order derivations of Rm , is a rational function under some conditions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:: Let R be a coordinate ring of an affine irreducible curve represented by k[x1,x2,...,xs] (f) and m be a maximal ideal of R.
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Key Findings & Data:In this article, the Betti series of Ω2(Rm) is studied.
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Conclusion & Impact:We proved that the Betti series of Ω2(Rm), where Ω2(Rm) denotes the universal module of second order derivations of Rm , is a rational function under some conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

: Let R be a coordinate ring of an affine irreducible curve represented by k[x1,x2,...,xs] (f) and m be a maximal ideal of R. In this article, the Betti series of Ω2(Rm) is studied. We proved that the Betti series of Ω2(Rm), where Ω2(Rm) denotes the universal module of second order derivations of Rm , is a rational function under some conditions.

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Cite This Article

ERDOGAN, A., TEKIN, H. M. A. (2022). On Betti series of the universal modules of second order derivations of k[x1,x2,...,xs] (f). Turkish Journal of Mathematics, Cilt: 38 - Sayı: 1, 25–28. https://ajindex.com/articles/608268

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References (5)

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  3. Erdoğan, A.: Homological dimension of the universal modules for hypersurfaces. Comm. Algebra 24(5), 1565-1573 (1996).
  4. Kunz, E.: Introduction to Commutative Algebra and Algebraic Geometry. Boston: Birkhauser 1985.
  5. Nakai, Y.: High order derivations 1. Osaka J.Math. 7, 1-27 (1970).