Growth and Relations in Graded Rings
| dc.creator | Piontkovsky, Dmitri | |
| dc.date | 1999-03-05 | |
| dc.date.accessioned | 2026-07-07T05:28:13Z | |
| dc.date.available | 2026-07-07T05:28:13Z | |
| dc.description | Suppose $A$ is a graded associative algebra over a field, $I$ is its ideal generated by a set $α$ of homogeneous elements, and B = A/I. In this note, some inequalities between Hilbert series of algebras $A,B$ and the number of elements of the set $α$ are announced. As in the Golod--Shafarevich inequality as in our case the equality in every estimate is exact iff the set $α$ is strongly free: so we obtain some new characterizations of such sets. As a consequence it is proved that over a field of zero characteristic for the class of finitely defined graded algebras there is no algorithm to answer the following question: for an algebra $A$ and a rational number $R$, is the convergence radius of the Hilbert series of $A$ equal to $R$? | |
| dc.description | 17 pages in Latex2e, To appear in Proc. of Moscow-Tainan Algebraic Workshop | |
| dc.identifier | https://arxiv.org/abs/math/9903030 | |
| dc.identifier | http://arxiv.org/abs/math/9903030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78178 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W50 | |
| dc.title | Growth and Relations in Graded Rings | |
| dc.type | text |