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All these problems have height 1.
- a) use and
- b) notice x,y map to units
- c) use the result that after a linear change of variable any conic can be expressed as a hyperbola, ellipse, or parabola.
- Show then find an isomorphism with and to show the dimension is 1.
- Use basic rules about products of ideals an intersections to show
- Check each term in the union if the vanishing of a prime ideal.
- A base for the topology of consists of sets where each are open in the cofinite topology of
- Compare an open set like with a open set like