# Vénéreau-type polynomials as potential counterexamples

```@article{Lewis2010VnreautypePA,
title={V{\'e}n{\'e}reau-type polynomials as potential counterexamples},
author={Drew Lewis},
journal={Journal of Pure and Applied Algebra},
year={2010},
volume={217},
pages={946-957}
}```
• D. Lewis
• Published 14 July 2010
• Mathematics
• Journal of Pure and Applied Algebra
• Mathematics
Annales de la Faculté des sciences de Toulouse : Mathématiques
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## References

SHOWING 1-10 OF 17 REFERENCES

• Mathematics
• 2001
The Abhyankar-Sathaye Problem asks whether any biregular embedding φ: C k → C n can be rectified, that is, whether there exists an automorphism a E Aut C n such that a o φ is a linear embedding. Here
A coordinate is an element of a polynomial ring which is the first component of some automorphism of this ring. Understanding the structure of coordinates is still one of the major problems in the
• Mathematics
• 1976
of a finitely generated projective K-module P. This result, to which the title refers, is contained in Theorem (4.4) below. Geometrically it asserts that every locally trivial fibre space over
• Mathematics
• 2010
This paper gives a method of constructing affine fibrations for polynomial rings. The method can be used to construct the examples of \(\mathbb {A}\) 2-fibrations in dimension 4 due to Bhatwadekar
Dans un anneau de polynomes a \$n\$ indeterminees \$A\n=A[y_1\tr y_n]\$ a coefficients dans un anneau commutatif unitaire \$A\$ on dit qu'un polynome \$p=p(y_1\tr y_n)\$ est une variable ou \$A\$-variable s'il