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  "body": "\n## Summary\n\nA graded ring is a [[ring|0B1261B5ED]] that splits as a direct sum of pieces $R_0, R_1, R_2, \\dots$.\nThe product of an element of $R_m$ and an element of $R_n$ must lie in $R_{m+n}$.\nThe main example is a polynomial ring, split by degree.\nGraded rings are the algebraic side of projective geometry, and they appear in commutative algebra through [[associated graded rings|8HFAEGFQT1]] and [[Rees algebras|W8ZAH8TTHS]].\n\n## Explanations\n\n### L1 human\n\nIn a polynomial ring every polynomial is a sum of homogeneous parts, one for each degree.\nMultiplying two homogeneous parts adds their degrees.\nA graded ring is any ring with this kind of bookkeeping by degree.\nFor example, $x^2 + 3xy + 5$ in $k[x, y]$ has a part $x^2 + 3xy$ of degree $2$ and a part $5$ of degree $0$.\nThe [[definition|CAPQBQDRA7]] makes this precise.\n",
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