Journal of Commutative Algebra

On codimension-one $\A^1$-fibration with retraction

Article information

Source
J. Commut. Algebra, Volume 3, Number 2 (2011), 207-224.

Dates
First available in Project Euclid: 24 June 2011

https://projecteuclid.org/euclid.jca/1308935128

Digital Object Identifier
doi:10.1216/JCA-2011-3-2-207

Mathematical Reviews number (MathSciNet)
MR2813472

Zentralblatt MATH identifier
1241.13004

Citation

Das, Prosenjit; Dutta, Amartya K. On codimension-one $\A^1$-fibration with retraction. J. Commut. Algebra 3 (2011), no. 2, 207--224. doi:10.1216/JCA-2011-3-2-207. https://projecteuclid.org/euclid.jca/1308935128

References

• Teruo Asanuma, Polynomial fibre rings of algebras over Noetherian rings, Invent. Math. 87 (1987), 101-127.
• S.M. Bhatwadekar and Amartya K. Dutta, On $\A^1$-fibrations of subalgebras of polynomial algebras, Comp. Math. 95 (1995), 263-285.
• S.M. Bhatwadekar, Amartya K. Dutta and Nobuharu Onoda, On algebras which are locally $\A^1$ in codimension-one, Trans. Amer. Math. Soc., to appear.
• Amartya K. Dutta, On $\A^1$-bundles of affine morphisms, J. Math. Kyoto Univ. 35 (1995), 377-385.
• Amartya K. Dutta and Nobuharu Onoda, Some results on codimension-one $\A^1$-fibrations, J. Algebra 313 (2007), 905-921.
• Paul Eakin and James Silver, Rings which are almost polynomial rings, Trans. Amer. Math. Soc. 174 (1972), 425-449.
• Cornelius Greither, A note on seminormal rings and $\A^1$-fibrations, J. Algebra 99 (1986), 304-309.
• Eloise Hamann, On the $R$-invariance of $R[x]$, J. Algebra 35 (1975), 1-16.
• Hideyuki Matsumura, Commutative ring theory, second ed., Cambridge Stud. Adv. Math. 8, Cambridge University Press, Cambridge, 1989, translated from the Japanese by M. Reid.
• Nobuharu Onoda, Subrings of finitely generated rings over a pseudogeometric ring, Japan. J. Math. %(N.S.) 10 (1984), 29-53.
• Richard G. Swan, On seminormality, J. Algebra 67 (1980), 210-229.
• Joe Yanik, Projective algebras, J. Pure Appl. Algebra 21 (1981), 339-358.