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- A graded ring is a commutative ring containing 1, in which a family of additive subgroups is specified such that R is the direct sum of these subgroups12. The polynomial ring is graded by degree, and the localization of a graded integral domain R with respect to the set of all nonzero homogeneous elements in R is a graded ring3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.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/2034872By 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
Homogenous localization and usual localization in graded rings
See results only from math.stackexchange.comGraded rings and their loc…
Let $A$ be a $\mathbb{Z}_{\geq 0}$-graded ring, $f \in A$ - homogenious, and $I …
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A G-graded ring $R$ is a ring, also denoted by $R$, together with a direct sum …
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