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- Title
Bounds and definability in polynomial rings.
- Authors
ASCHENBRENNER, MATTHIAS
- Abstract
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 flavour. In particular, we show that the module of syzygies of polynomials f1,… , fn∈R[X1,… ,XN] 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 fj. This implies that if R is a Bézout domain, then the generators can be parametrized in terms of the coefficients of f1,… , fn using the ring operations and a certain division function, uniformly in R.
- Subjects
DEFINABILITY theory (Mathematical logic); POLYNOMIAL rings; RING theory; PARAMETER estimation; ALGEBRAIC fields
- Publication
Quarterly Journal of Mathematics, 2005, Vol 56, Issue 3, p263
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hah048