Element Outside $\mathfrak{m}_p^2$ Generates $\mathfrak{m}_p$ Algebraic Geometry Image of the Segre Embedding Algebraic Geometry Maximal Ideals of the Polynomial Ring Algebraic Geometry Projective Hypersurfaces Always Intersect Algebraic Geometry Bézout for Lines Algebraic Geometry Sum of Orders Is Zero Algebraic Geometry Nonconstant Morphism Induces a Finite Field Extension Algebraic Geometry Projective Closure of an Affine Variety via Homogenisation of the Ideal Algebraic Geometry