Hilbert Polynomials for the Extension Functor
نویسنده
چکیده
Let R be a local ring, I ⊆ R an ideal, and M and N finite Rmodules. In this paper we provide a number of results concerning the degree of the polynomial giving the lengths of the modules ExtR(N/I nN, M), when such a polynomial exists. Included among these results are a characterization of when this degree equals the Krull dimension of R, a characterization of when the degree of the polynomial associated to the first non-vanishing Ext under consideration equals the grade of I on M , and calculation of the degree of Hilbert polynomials associated to certain iterated expressions involving the extension functor.
منابع مشابه
Hilbert-samuel Polynomials for the Contravariant Extension Functor
Let (R, m) be a local ring and M and N finite R-modules. In this paper we give a formula for the degree of the polynomial giving the lengths of the modules ExtR(M, N/m nN). A number of corollaries are given and more general filtrations are also considered.
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