Truncations of the ring of number-theoretic functions

1999/04/30 by Jan Snellman
Mathematics · #math.AC #msc:13Dxx #msc:10.00

paper · pdf

published as Homology, Homotopy and Applications, volume 2, pp 17-27, 2000 · 10 pages, no figures, 3 tables

arxiv created 2000/02/03 · arxiv updated 2009/11/30

Abstract

We study the ring of all functions from the positive integers to some field. This ring, which we call the ring of number-theoretic functions, is an inverse limit of the ``truncations'' Γ_n consisting of all functions f for which f(m)=0 whenever m > n. Each Γ_n is a zero-dimensional, finitely generated (K)-algebra, which may be expressed as the quotient of a finitely generated polynomial ring with a reversely stable monomial ideal. Using the description of the free minimal resolution of stable ideals, given by Eliahou-Kervaire, and some additional arguments by Aramova-Herzog and Peeva, we give the Poincaré-Betti series for Γ_n.

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