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Corrections to My Paper “On Krull’s Conjecture Concerning Valuation Rings”

Published online by Cambridge University Press:  22 January 2016

Masayoshi Nagata
Masayoshi Nagata*
Affiliation:
Mathematical Institute, Kyoto University
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The proof of Theorem 1 in the paper “On Krull’s conjecture concerning valuation rings” (vol. 4 (1952) of this journal) is not correct. We want to give here a corrected proof of the theorem: From p. 30, l. 14 to p. 31, l. 7 should be changed as follows.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 209 - 212
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

1) Prof. P. Ribenboim has communicated to the writer that the proof is not correct. The writer is grateful to him for his kind communication.

2) Such elements e*, e″ and so on exist because K is algebraically closed and therefore the residue class field of the valuation ring of w is algebraically closed (and contains infinitely many elements).

3) If we take σ**, in this case, to be any number in G which is greater than σ*, then we see also the proof by the same way as below.