Let a be an algebraic integer and suppose that f(a)=0, where f(x) in Q[x] is irreducible and monic. Show that f(x) in Z[x]. Please help me, thanks so much!
Let a be an algebraic integer and suppose that f(a)=0, where f(x) in Q[x] is irreducible and monic. Show that f(x) in Z[x]. Please help me, thanks so much!
What have you done so far? The key point is really that a is the root of some monic polynomial, g(x), with coefficients in Z. You need to show that f(x)=g(x).