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A Theorem on Finite Generation of a Ring

Published online by Cambridge University Press:  22 January 2016

Masayoshi Nagata
Masayoshi Nagata*
Affiliation:
Kyoto University
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The fourteenth problem of Hilbert asked finite generation of a certain class of rings and had a counter-example (cf. [4]). On the other hand, many mathematicians gave various sufficient conditions for finite generation of such rings (see, for instance, [9], [5] and [8]). The purpose of the present paper is to give a new sufficient condition. The class of rings to be treated is much more general than those treated before, except for the one in [8].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 193 - 205
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Grothendieck, A., Eléments de géométrie algébrique, Publ. Math. Inst. Etudes Sci. No. 4 (1960).Google Scholar
[2] Grothendieck, A., Seminaire de géométrie algébrique 1961, Inst. Haut. Etudes Sci.Google Scholar
[3] Nagata, M., A treatise on the 14-th problem of Hilbert, Mem. Coll. Sci. Univ. Kyoto, Ser. A Math. 30 (1956–57), 57–70. Addition and corrections, ibid. 197–200.Google Scholar
[4] Nagata, M., On the fourteenth problem of Hilbert, Proc. Internat. Congress of Math. 1958, Cambridge Univ. Press (1960), 459–462.Google Scholar
[5] Nagata, M., On the fourteenth problem of Hilbert, Lecture notes (by Murthy) at Tata Inst. F. R., forthcoming.Google Scholar
[6] Nagata, M., Invariants of a group in an affine ring, J. Math. Kyoto Univ. 3 (1963–64), 369–377.Google Scholar
[7] Nagata, M., Local rings, Intersci. Tracts 13, John Wiley (1962).Google Scholar
[8] Nagata, M., Miyata, T., Remarks on matric groups, J. Math. Kyoto Univ. 4 (1964–65), 381–384.Google Scholar
[9] Weyl, H., Classical groups, Princeton Univ. Press (1939).Google Scholar
[10] Zariski, O., Interprétations algébrico-géométriques du quatorziéme problème de Hilbert, Bull. Sci. Math. 78 (1954), 155–168.Google Scholar