Truncations of the ring of number-theoretic functions
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Publication:1977362
DOI10.4310/HHA.2000.V2.N1.A2zbMATH Open1002.11004arXivmath/9904143MaRDI QIDQ1977362
Publication date: 11 May 2000
Published in: Homology, Homotopy and Applications (Search for Journal in Brave)
Abstract: We study the ring of all functions from the positive integers to some field. This ring, which we call emph{the ring of number-theoretic functions}, is an inverse limit of the ``truncations Gamma_n consisting of all functions f for which f(m)=0 whenever m > n. Each Gamma_n is a zero-dimensional, finitely generated (K)-algebra, which may be expressed as the quotient of a finitely generated polynomial ring with a emph{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 Poincar'e-Betti series for Gamma_n.
Full work available at URL: https://arxiv.org/abs/math/9904143
Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Syzygies, resolutions, complexes and commutative rings (13D02) Arithmetic functions; related numbers; inversion formulas (11A25)
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