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arXiv · 1212.6501

A note on rigidity and triangulability of a derivation

Manoj K. Keshari·Swapnil A. Lokhande
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Abstract

Let A be a $\mathfrak Q$-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.

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Manoj K. Keshari, Swapnil A. Lokhande. 2012-12-28. A note on rigidity and triangulability of a derivation. https://arxiv.org/abs/1212.6501

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