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

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References

SHOWING 1-10 OF 17 REFERENCES

Simple birational extensions of the polynomial algebra C[3]

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

Polynomial coordinates and their behavior in higher dimensions

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

Locally polynomial algebras are symmetric algebras

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

Families of Affine Fibrations

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

Automorphismes et variables de l'anneau de polynômes A[y_1,...,y_n]

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

Polynomial fibre rings of algebras over noetherian rings