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  2. By a graded ring we mean a commutative ring R, containing 1, in which a family of additive subgroups Ri, i run- ning through the group Z of integers, is specified such that (i) as additive group, R is the (weak) direct sum Z>.CO Ri, (ii) RiRkCRi+k for any i, kECZ. The elements of Ri are said to be homogeneous of degree i.
    www.jstor.org/stable/2034872
    By a graded ring we mean a commutative ringR, containing 1, in which a family of additive subgroups £,, i run-ning through the group Z of integers, is specified such that as additive group, R is the (weak) direct sum /*„ _, £<, RiRkQRi+k for any i, k^Z.
    www.ams.org/journals/proc/1961-012-05/S0002-99…
    The polynomial ring is graded by degree: it is a direct sum of consisting of homogeneous polynomials of degree i. Let S be the set of all nonzero homogeneous elements in a graded integral domain R. Then the localization of R with respect to S is a -graded ring.
    en.wikipedia.org/wiki/Graded_ring
     
  3. Graded ring - Wikipedia

  4. Section 27.8 (01M3): Proj of a graded ring—The Stacks project

  5. Section 10.56 (00JL): Graded rings—The Stacks project

  6. Graded rings and their localizations - Mathematics Stack Exchange

  7. Localization in graded rings - Mathematics Stack Exchange

  8. 8. Localization of Graded Rings - SpringerLink

  9. Methods of Graded Rings - SpringerLink

  10. Graded rings and maximal ideals of a local ring

  11. Section 10.57 (00JM): Proj of a graded ring—The Stacks project

  12. EM− Graded Rings - Alraqad - 2024 - Wiley Online Library

  13. abstract algebra - Localization of a graded ring at degree zero ...

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