## Nihonkai Mathematical Journal

### The automorphism theorem and additive group actions on the affine plane

Shigeru Kuroda

#### Abstract

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.

#### Note

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

#### Article information

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

Dates
First available in Project Euclid: 7 March 2018

https://projecteuclid.org/euclid.nihmj/1520391684

Mathematical Reviews number (MathSciNet)
MR3771369

Zentralblatt MATH identifier
06881243

#### Citation

Kuroda, Shigeru. The automorphism theorem and additive group actions on the affine plane. Nihonkai Math. J. 28 (2017), no. 1, 65--68. https://projecteuclid.org/euclid.nihmj/1520391684

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