Abstract
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 14th 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 \( {\mathbbm{G}}_a \)-action on R[X, Y, Z] for an affine Dedekind domain R using topological methods.
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R. V. Gurjar is thankful to the Department of Atomic Energy of the Govt. of India for Dr. Raja Ramanna Fellowship.
S. R. Gurjar is thankful to the INSPIRE Fellowship of the Department of Science & Technology of the Govt. of India.
B. Hajra is thankful to the UGC-NET Scholarship of the Govt. of India.
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GURJAR, R.V., GURJAR, S.R. & HAJRA, B. ZARISKI’S FINITENESS THEOREM AND PROPERTIES OF SOME RINGS OF INVARIANTS. Transformation Groups 26, 1315–1329 (2021). https://doi.org/10.1007/s00031-020-09594-0
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DOI: https://doi.org/10.1007/s00031-020-09594-0