RESULTS ON BETTI SERIES OF THE UNIVERSAL MODULES OF SECOND ORDER DERIVATIONS

Erdogan A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.40, no.3, pp.449-452, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2011
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.449-452
  • Hacettepe University Affiliated: Yes

Abstract

Let R be the coordinate ring of an affine irreducible curve presented by 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.