Nihonkai Mathematical Journal

The automorphism theorem and additive group actions on the affine plane

Shigeru Kuroda

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Due to Rentschler, Miyanishi and Kojima, the invariant ring for a $\mathrm{G}_a$-action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we give a new short proof for this result using the automorphism theorem of Jung and van der Kulk.


Partly supported by JSPS KAKENHI Grant Numbers 15K04826, 24340006.

Article information

Nihonkai Math. J., Volume 28, Number 1 (2017), 65-68.

Received: 14 April 2016
First available in Project Euclid: 7 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 14R20: Group actions on affine varieties [See also 13A50, 14L30]

additive group action affine plane polynomial ring polynomial automorphism Jung-van der Kulk theorem Rentschler theorem


Kuroda, Shigeru. The automorphism theorem and additive group actions on the affine plane. Nihonkai Math. J. 28 (2017), no. 1, 65--68.

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