English

Tame and wild degree functions

Algebraic Geometry 2010-07-06 v1 Commutative Algebra

Abstract

We give examples of degree functions deg : R --> M, where R is a polynomial ring in 2 or 3 variables and M is either the integers or the natural numbers, whose behaviour with respect to derivations D : R --> R is pathological in the sense that deg(Dx) - deg(x) (where x in R \ {0}) is not bounded above. We also give several general results stating that such pathologies do not occur when the degree functions satisfy certain hypotheses.

Keywords

Cite

@article{arxiv.1007.0508,
  title  = {Tame and wild degree functions},
  author = {Daniel Daigle},
  journal= {arXiv preprint arXiv:1007.0508},
  year   = {2010}
}

Comments

25 pages

R2 v1 2026-06-21T15:44:09.548Z