Nagoya Mathematical Journal

On separable $\bold A\sp 1$-forms

Amartya Kumar Dutta

Full-text: Open access

Abstract

We show that for any field $k$, separable $\mathbb{A}^1$-forms over commutative $k$-algebras are trivial.

Article information

Source
Nagoya Math. J., Volume 159 (2000), 45-51.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631451

Mathematical Reviews number (MathSciNet)
MR1783563

Zentralblatt MATH identifier
0962.13016

Subjects
Primary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Secondary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13C10: Projective and free modules and ideals [See also 19A13]

Citation

Dutta, Amartya Kumar. On separable $\bold A\sp 1$-forms. Nagoya Math. J. 159 (2000), 45--51. https://projecteuclid.org/euclid.nmj/1114631451


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References

  • H. Bass, E. H. Connell and D. L. Wright, Locally polynomial algebras are symmetric algebras. , Invent. Math., 38 (1977), 279–299.
  • S. M. Bhatwadekar, A. K. Dutta, On $\BA^1$-fibrations of subalgebras of polynomial algebras , Comp. Math., 95(3) (1995), 263–285.
  • S. Itoh, On Weak Normality and Symmetric Algebras , J. Algebra, 85(1) (1983), 40–50.
  • H. Matsumura, Commutative Algebra, Benjamin, 2nd Edn. (1980).
  • T. Kambayashi, On the absence of nontrivial separable forms of the affine plane , J. Algebra, 35 (1975), 449–456.
  • A. Sathaye, Polynomial Ring in Two Variables over a D.V.R.:A Criterion , Invent. Math., 74 (1983), 159–168.