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?