Graded ring

Summary

A graded ring is a ring that splits as a direct sum of pieces $R_0, R_1, R_2, \dots$. The product of an element of $R_m$ and an element of $R_n$ must lie in $R_{m+n}$. The main example is a polynomial ring, split by degree. Graded rings are the algebraic side of projective geometry, and they appear in commutative algebra through associated graded rings and Rees algebras.