Editing Polynomial ring (section)

==Graded structure==
Every polynomial ring is a [[graded ring]]: one can write the polynomial ring <math>R = K[X_1, \ldots, X_n]</math> as a [[direct sum]]
<math display=block> R = \bigoplus_{i = 0}^\infty R_i</math>
where <math>R_i</math> is the subspace consisting of all [[homogeneous polynomial]]s of degree <math>i</math> (along with the zero polynomial); then for any elements <math>f \in R_i</math> and <math>g \in R_j</math>, their product <math>fg</math> belongs to <math>R_{i + j}</math>.