Is it possible ?



Need an example of  not finitely generated graded algebra such that its  Poincaré series is a rational function.
Rather obviously yes.


Let $A$ be the algebra over the field $K$ generated by elements $a\_1,a\_2,\ldots,$
with $a\_i$ in dimension $i$ and with $a\_ia\_j=0$ for all $i$ and $j$.
This is an incredibly uninteresting example, but since each graded piece
is one-dimensional, its Poincare series is $\sum\_{n=0}^\infty t^n=1/(1-t)$.


