Lets cover some background around Chinese Remaindering and homomorphisms of rings – Consider , a monic polynomial of degree N that splits into r distinct irreducible factors of degree d = N/r, viz. . (In the case of mod 2 we have . Let denote the ring which is the quotient of modu...
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...