Finite generation of certain subrings

Finite generation of certain subrings
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Proc. Amer. Math. Soc. 99 (1987), 201-204 Request permission

A more geometric approach can be used to prove finite generation of certain subrings, notably invariants under reductive group actions.

References

Paul M. Eakin Jr., The converse to a well known theorem on Noetherian rings, Math. Ann. 177 (1968), 278–282. MR 225767, DOI 10.1007/BF01350720
John Fogarty, Kähler differentials and Hilbert’s fourteenth problem for finite groups, Amer. J. Math. 102 (1980), no. 6, 1159–1175. MR 595009, DOI 10.2307/2374183
John Fogarty, Geometric quotients are algebraic schemes, Adv. in Math. 48 (1983), no. 2, 166–171. MR 700982, DOI 10.1016/0001-8708(83)90086-5
David Mumford, Hilbert’s fourteenth problem–the finite generation of subrings such as rings of invariants, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc.., Providence, R.I., 1976, pp. 431–444. MR 0435076
David Mumford and John Fogarty, Geometric invariant theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 34, Springer-Verlag, Berlin, 1982. MR 719371, DOI 10.1007/978-3-642-96676-7