Need an example of finitely generated graded algebra such that each its graded subspace has infinite dimension. - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T03:21:02Z http://mathoverflow.net/feeds/question/41195 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/41195/need-an-example-of-finitely-generated-graded-algebra-such-that-each-its-graded Need an example of finitely generated graded algebra such that each its graded subspace has infinite dimension. Melania 2010-10-05T18:57:07Z 2010-10-17T10:20:41Z <p>More accurately, let $\displaystyle A=\sum_{i=0}^{\infty}A_i$ be a finitely generated graded algebra over say $\mathbb{Q}$ but $\dim A_i=\infty$ for each $i.$ Is it possible?</p> http://mathoverflow.net/questions/41195/need-an-example-of-finitely-generated-graded-algebra-such-that-each-its-graded/41196#41196 Answer by AndrĂ© Henriques for Need an example of finitely generated graded algebra such that each its graded subspace has infinite dimension. AndrĂ© Henriques 2010-10-05T19:05:33Z 2010-10-05T20:01:00Z <p>$\mathbb Q[x,y]$ with $x$ in degree 0, and $y$ in degree 1.<br></p> <p>If you want your generators to be in positive degrees, then what you're asking for is impossible.</p>