English

A note on rigidity and triangulability of a derivation

Commutative Algebra 2014-08-13 v1

Abstract

Let A be a Q\mathfrak Q-domain, K=frac(A), B=A^{[n]} and D\in \lnd_A(B). Assume rank D= rank D_K=r, where D_K is the extension of D to K^{[n]}. Then we show that (i) If D_K is rigid, then D is rigid. (ii) Assume n=3, r=2 and B=A[X,Y,Z] with DX=0. Then D is triangulable over A if and only if D is triangulable over A[X]. In case A is a field, this result is due to Daigle.

Cite

@article{arxiv.1212.6501,
  title  = {A note on rigidity and triangulability of a derivation},
  author = {Manoj K. Keshari and Swapnil A. Lokhande},
  journal= {arXiv preprint arXiv:1212.6501},
  year   = {2014}
}

Comments

5 page

R2 v1 2026-06-21T23:01:11.524Z