Bounds and definability in polynomial rings
| dc.creator | Aschenbrenner, Matthias | |
| dc.date | 2003-06-16 | |
| dc.date.accessioned | 2026-07-07T04:58:59Z | |
| dc.date.available | 2026-07-07T04:58:59Z | |
| dc.description | We study questions around the existence of bounds and the dependence on parameters for linear-algebraic problems in polynomial rings over rings of an arithmetic flavor.In particular, we show that the module of syzygies of polynomials $f_1,...,f_n\in R[X_1,...,X_N]$ with coefficients in a Prüfer domain $R$ can be generated by elements whose degrees are bounded by a number only depending on $N$, $n$ and the degree of the $f_j$. This implies that if $R$ is a Bézout domain, then the generators can be parametrized in terms of the coefficients of $f_1,...,f_n$ using the ring operations and a certain division function, uniformly in $R$. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306240 | |
| dc.identifier | http://arxiv.org/abs/math/0306240 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67802 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Logic | |
| dc.subject | Primary 13D02; Secondary 13F05, 13L05 | |
| dc.title | Bounds and definability in polynomial rings | |
| dc.type | text |