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Dergiler / 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
Sayfa
25–28
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez:: 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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Temel Bulgular & Veri:In this article, the Betti series of Ω2(Rm) is studied.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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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Bu Makaleye Atıf Yap

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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Kaynakça (5)

  1. Çimen, N., Erdoğan, A.: Projective dimension of the universal modules for the product of a hypersurface and affine t-space. Comm. Algebra 27(10), 4737-4741 (1999).
  2. Erdoğan, A.: Results on Betti series of the universal modules of the second order derivation. Hacet.J.Math. Stat. 40(3), 449-452 (2011).
  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).