A. ERDOĞAN

5468

Result on Betti series of the universal modules of second order derivations

Result on Betti series of the universal modules of second order derivations

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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  • [1]Erdoğan, A. Homological dimension of the universal modules for hypersurfaces, Comm. Algebra 24(5), 1565-1573, 1996.
  • [2]Nakai, Y. High order derivations 1, Osaka J. Math. 7, 1-27, 1970.
  • [3]Sweedier, M.E. and Heynemann, R.G. Affine Hopf algebras, J. Algebra 13, 192-241, 1969.
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: 6
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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