THE RING OF ARITHMETICAL FUNCTIONS WITH

Abstract. Let (A; +;) denote the ring of arithmetical functions with unitary convolution, and let V + have the property that for every v 2 V, all unitary divisors of v lie in V. If in addition V is nite, thenAV is an artinian monomial quotient of a polynomial ring in nitely many indeterminates, and isomorphic to the \Artinied " Stanley-Reisner ring [(V)] of a certain simplicial complex (V). We describe some ring-theoretical and homological properties of AV. 1