Suppose that E is a free module with basis (ai)i∈ I and let (bi)i∈ I be a family of elements of F. Then, there exists a unique R-homomorphism f : E→ F such that f (ai) = bi, ∀i∈ I. Proof.– Let x=∑i∈Iλi.ai be an arbitrary element of E. Then, fx=∑i...
First we note that the map [Math Processing Error]t↦∑i≤mtiai is a well-defined surjective [Math Processing Error]OK-module homomorphism from [Math Processing Error]OKm to [Math Processing Error]OK/qOK, with kernel [Math Processing Error]a⊥. The distance to uniformity of [Math Processin...