The ring of arithmetical functions with unitary convolution: General Truncations

2002/05/23 by Jan Snellman
Mathematics · #math.AC #msc:11A25 #msc:13J05

paper · pdf

published as Int. J. Math. Game Theory Algebra 13 (2003), no. 6, 485--519 · 27 pages, LaTeX2e

arxiv created 2002/05/23 · arxiv updated 2009/11/30

Abstract

Let A denote the ring of arithmetical functions with unitary convolution, and let V be a finite subset of the positive integers having the property that for every v in V, all unitary divisors of v lie in V. We study the truncation A_V, an artinian monomial quotient of a polynomial ring in finitely many indeterminates, isomorphic to the ``Artinified'' Stanley-Reisner ring C[Δ(V)] of a certain simplicial complex Δ(V).

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