most recent 30 from http://mathoverflow.net 2013-05-25T10:47:02Z http://mathoverflow.net/feeds/question/68084 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68084/graded-noetherian-module mark 2011-06-17T19:56:58Z 2011-07-29T22:22:12Z

<p>Let M be a R graded module with $M= \oplus M_i$. If M is noetherian then $M_i=0 $ for i &lt;&lt; 0. My question is this, isn't $M_i = 0$ for all i >> 0 as well? If $(M_{n_i})_{i} \neq 0, n_i > 0$ then $M_{n_1} \nsubseteq M_{n_1} \oplus. .. M_{n_2} \nsubseteq M_{n_1} \oplus. .. M_{n_2} \oplus. .. M_{n_3} \nsubseteq. ..$ isn't a contradiction with ACC rule?</p>

http://mathoverflow.net/questions/68084/graded-noetherian-module/68089#68089 Mariano Suárez-Alvarez 2011-06-17T20:06:07Z 2011-06-17T20:06:07Z

<p>Pick your favorite noetherian graded ring $R$, and consider the free module $M=R$. Are you saying it must vanish in high degree?</p>