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Apr 13, 2017 at 12:19 history edited CommunityBot
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Nov 3, 2012 at 20:09 history edited user26857 CC BY-SA 3.0
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Oct 20, 2012 at 9:50 comment added Ralph Isn't a graded $K$-algebra also a graded ring ? -:) I actually find this "controvery" useful, as some readers might recognize that using a short additional attribute like "positively graded" or "$\mathbb{N}$-graded" (in contrast to a single "graded") helps to avoid confison. BTW: That's exactly what Bruns does in the liked paper.
Oct 18, 2012 at 18:09 comment added Ralph @navigetor23: Bruns-Herzog, Def. 1.5.1: "A graded ring is a ring together with a decomposition $R=\bigoplus_{i \in \mathbb{Z}}R_i$ such that $R_iR_j\subset R_{i+j}$ for all $i,j \in \mathbb{Z}$." Therefore I doubt that your "kind of standard terminology in commutative algebra" is actually standard.
Oct 18, 2012 at 14:57 comment added Fred Rohrer Dear @navigetor23, this might be a reasonable abuse of language within a certain book or even community, but in general it is just totally unclear and moreover prone to mistakes.
Oct 18, 2012 at 13:34 comment added Karl Schwede Dear @navigetor23, you have to have at least 50 reputation to leave comments I believe.
Oct 18, 2012 at 12:06 comment added Fred Rohrer Dear @navigetor23, it might be helpful if you would specify what kind of graduations (positive,...) you consider, and which kind of finiteness hypotheses you make. (I guess you need $R$ to be coherent and $M$ to be of finite presentation.)
Oct 18, 2012 at 11:49 history edited user26857 CC BY-SA 3.0
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Oct 18, 2012 at 9:43 history edited user26857 CC BY-SA 3.0
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Oct 18, 2012 at 9:25 history answered user26857 CC BY-SA 3.0