Lemmas in algebra

theorem to simplify sums of products of sequences

lemma that the greatest common divisor of the coefficients is a multiplicative function

lemma

theorem in commutative algebra

theorem

lemma stating that, given an ideal I in a Noetherian commutative ring R and a submodule N of a a finitely generated R-module M, there exists a positive integer k such that, for every n≥k, IⁿM ∩ N = Iⁿ⁻ᵏ(IᵏM ∩ N)