The formal Dirichlet series form a ring Ω, indeed an "R"-algebra, with the zero function as additive zero element and the function δ defined by "δ"(1) = 1, "δ"("n") = 0 for "n" > 1 as multiplicative identity. An element of this ring is invertible if "a"(1) is invertible in "R". If "R" is commutative, so is Ω; if "R" is an integral domain, so is Ω. The non-zero multiplicative functions form a subgroup of the group of units of Ω.