Assume that a positively graded ring R is generated in degree 1. Is it true that, if R is Cohen-Macaulay, then there exists a regular sequence **x** of elements of degree 1 so that R/**x** is zero dimensional? 


I tend to believe that it holds, but could not find a reference. Maybe some extra condition should be imposed? 



Regular sequence of elements of degree 1 for a homogeneous Cohen-Macaulay ring
You want to assume also that the residue field is infinite. Then a minimal reduction of the irrelevant ideal will be a system of parameters, each linear, and will be a maximal regular sequence.


