2
$\begingroup$

I am so sorry if you feel this kind of question is not appropriate for MS. But I hope you can sympathize with me, I tried to find the answer in all my books and even Google but I found nothing.

My question is : What is a standard graded algebra over a ring?

Please help me. Thanks.

Edit:

In the following paper On the asymtotic linearity of Castelnuovo-Mumford regularity, there is a definition of standard graded algebra. Suppose that $A$ is a ring, $R$ is a standard graded $A$ algebra if $R_{0}=A$ and $R$ is generated by the element of $R_1$. I did not fully understand this definition. Can anyone give here an example?

  • 2
    More context please. I would guess from the commutative algebra tag that the polynomial ring over that field would be a good guess though.2012-04-18
  • 2
    I am pretty awful at searching. But out of curiosity I typed "standard graded algebra" (with quotes) in Google. Quite a few hits, including definitions.2012-04-18
  • 0
    Alex's example is an example of what's describe in your new edit.2012-04-18
  • 0
    @AndréNicolas Heh. When I type in "standard graded algebra" into Google, this question is the first result.2012-04-18
  • 0
    I have just added some new informations. Please help me.2012-04-18
  • 0
    Yes, AlexYoucis gave an example you want. $R=A[x,y]$ with the natural grading.2012-04-18
  • 0
    "Standard graded algebra" = "homogeneous algebra" in Bruns & Herzog terminology.2012-06-18

1 Answers 1