Homework for Week 12

1. An affine scheme X = Spec R is irreducible if and only if R has a unique minimal prime (equivalently, the nilradical of R is prime).
2. An affine scheme X = Spec R is reduced and irreducible if and only if R is a domain.
3. Define the disjoint union of two schemes. Show that the disjoint union of two affine schemes Spec R and Spec S is naturally identified with Spec (R x S).

Due Tuesday