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Generalized Nowicki conjecture
- Source :
- Proceedings of the American Mathematical Society. 148:3705-3711
- Publication Year :
- 2020
- Publisher :
- American Mathematical Society (AMS), 2020.
-
Abstract
- Let $B$ be an integral domain over a field $K$ of characteristic 0. The derivation $\delta$ of $B[Y_d]=B[y_1,\ldots,y_d]$ is elementary if $\delta(B)=0$ and $\delta(y_i)\in B$, $i=1,\ldots,d$. Then the elements $u_{ij}=\delta(y_i)y_j-\delta(y_j)y_i$, $1\leq i0$, $i=1,\ldots,d$, was handled by Khoury in the first proof of the Nowicki conjecture given by him in 2004. As a consequence of the proof of Kuroda in 2009 if $\delta(y_i)=f_i(x_i)$, for any nonconstant polynomials $f_i(x_i)$, $i=1,\ldots,d$, then $B[Y_d]^{\delta}=K[X_d,Y_d]^{\delta}$ is generated by $X_d$ and $U_d=\{u_{ij}=f_i(x_i)y_j-y_if_j(x_j)\mid 1\leq i<br />Comment: 7 pages LATEX
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 148
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....6d61661a9a4dd5f49b7f99884b564d0e