Algebraic number theory MOC

Gauß’s lemma

Suppose 𝑅 is a Unique factorization domain and 𝐹 =Frac⁡𝑅 is its Field of fractions. Then alg

1. The set of primitive polynomials in 𝑅[𝑥] is closed under multuplication;
2. 𝑓(𝑥) ∈𝑅[𝑥] is irreducible iff it is irreducible in 𝐹[𝑥] and primitive.

Proof

proof

---

develop | en | SemBr