ZARISKI’S FINITENESS THEOREM AND PROPERTIES OF SOME RINGS OF INVARIANTS

In this paper we will give a short proof of a special case of Zariski’s result about finite generation in connection with Hilbert’s 14 th problem using a new idea. Our result is useful for invariant subrings of unipotent or connected semisimple groups. We will also prove an analogue of Miyanishi’s result for the ring of invariants of a G a -action on R [ X , Y , Z ] for an affine Dedekind domain R using topological methods.