The irreducibility of symmetric Yagzhev maps
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- by Sławomir Bakalarski PDF
- Proc. Amer. Math. Soc. 138 (2010), 2279-2281 Request permission
Abstract:
Let $F:\mathbb {C}^n \rightarrow \mathbb {C}^n$ be a polynomial mapping in Yagzhev form, i.e. \[ F(x_1,\ldots ,x_n)=(x_1+H_1(x_1,\ldots ,x_n),\ldots ,x_n+H_n(x_1,\ldots ,x_n)),\] where $H_i$ are homogeneous polynomials of degree 3. We show that if $\mathrm {Jac}(F) \in \mathbb {C}^*$ and the Jacobian matrix of $F$ is symmetric, then the polynomials $x_i+H_i(x_1,\ldots ,x_n)$ are irreducible as elements of the ring $\mathbb {C}[x_1,\ldots ,x_n]$.References
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Additional Information
- Sławomir Bakalarski
- Affiliation: Institute of Computer Science, Jagiellonian University, Prof. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
- Email: Slawomir.Bakalarski@uj.edu.pl
- Received by editor(s): March 15, 2009
- Received by editor(s) in revised form: July 8, 2009
- Published electronically: March 10, 2010
- Communicated by: Martin Lorenz
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2279-2281
- MSC (2000): Primary 14R15, 12E05
- DOI: https://doi.org/10.1090/S0002-9939-10-10109-9
- MathSciNet review: 2607856