Nonconstant Morphism Induces a Finite Field Extension Algebraic Geometry Affine Pieces of Projective Varieties Are Affine Varieties Algebraic Geometry Characterisation of Local Rings Algebraic Geometry Irreducibility via Prime Ideals Algebraic Geometry Second Inequality Algebraic Geometry Complement of a Hypersurface is Affine Algebraic Geometry Krull's Height Theorem Algebraic Geometry Large Degree Implies Condition (*) Algebraic Geometry