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SPRING 2014 A note on rigidity and triangulability of a derivation
Manoj K. Keshari, Swapnil A. Lokhande
J. Commut. Algebra 6(1): 95-100 (SPRING 2014). DOI: 10.1216/JCA-2014-6-1-95

Abstract

Let $A$ be a $\q$-domain, $K=\text{frac\,}(A)$, $B=A^{[n]}$ and $D\in \text{LND}_A(B)$. Assume rank $D=\text{rank\,}D_K=r$, where $D_K$ is the extension of $D$ to $K^{[n]}$. Then we show that

\hskip5pt(i) If $D_K$ is rigid, then $D$ is rigid.

\hskip2.5pt(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. "A note on rigidity and triangulability of a derivation." J. Commut. Algebra 6 (1) 95 - 100, SPRING 2014. https://doi.org/10.1216/JCA-2014-6-1-95

Information

Published: SPRING 2014
First available in Project Euclid: 2 June 2014

zbMATH: 1327.14211
MathSciNet: MR3215562
Digital Object Identifier: 10.1216/JCA-2014-6-1-95

Subjects:
Primary: 14L30
Secondary: 13B25

Keywords: Locally nilpotent derivation , rigidity , triangulability

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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