2004/10/13 by Emanoil Theodorescu · 2 citations
Mathematics · #math.AC
published as Math. Proc. of the Cambridge Philos. Society (132) 2002
arxiv created 2004/10/13 · arxiv updated 2009/12/01
Let R be a commutative Noetherian ring, I an ideal, M and N finitely generated R-modules. Assume V(I)∩ Supp(M)∩ Supp(N) consists of finitely many maximal ideals and let ł(\ei(N/InN,M)) denote the length of \ei(N/InN,M). It is shown that ł(\ei(N/InN,M)) agrees with a polynomial in n for n>>0, and an upper bound for its degree is given. On the other hand, a simple example shows that some special assumption such as the support condition above is necessary in order to conclude that polynomial growth holds.