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

Authors : Ali ERDOĞAN

Pages : 449-452

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Publication Date : 2011-03-01

Article Type : Research Paper

Abstract :Let R be the coordinate ring of an affine irreducible curve presented by k[x,y] insert ignore into journalissuearticles values(f); and m a maximal ideal of R. Assume that Rm, the localization of R at m, is not a regular ring. Let Ω2insert ignore into journalissuearticles values(Rm); be the universal module of second order derivations of Rm. We show that, under certain conditions, Binsert ignore into journalissuearticles values(Ω2insert ignore into journalissuearticles values(Rm);, t);, the Betti series of Ω2insert ignore into journalissuearticles values(Rm);, is a rational function. To conclude, we give examples related to Binsert ignore into journalissuearticles values(Ω2insert ignore into journalissuearticles values(Rm);, t); for various rings R.
Keywords : Universal module, Universal differential operators, Betti series, Minimal resolution