Suppose is irreducible in .
1. Let (the ideal generated by ). Prove as additive abelian groups.
2. Show .
.
.
Define such that .
and , hence is a homomorphism.
Suppose , then which forces since we're working in an integral domain. Thus is injective.
given for some . So choose said to get . Hence is surjective.
Therefore is an isomorphism with for these additive groups.
Finally we get as additive abelian groups.
**For some reason I'm not too confident in this solution, so someone else might want to look it over.**