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A Note on Quotient Fields of Power Series Rings

Published online by Cambridge University Press:  20 November 2018

Huah Chu  and
Yi-Chuan Lang
Huah Chu
Affiliation:
Department of Mathematics, National Taiwan University Taipei, Taiwan 106 Republic of China
Yi-Chuan Lang
Affiliation:
Department of Mathematics, National Taiwan University Taipei, Taiwan 106 Republic of China
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Abstract

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Let R be an integral domain with quotient field K. If R has an overling S ≠ K, such that S[X] is integrally closed, then the "algebraic degree" of K((X)) over the quotient field of R[X] is infinite. In particular, it holds for completely integrally closed domain or Noetherian domain R.

Keywords

13F2512F0513B22power series ringquotient fieldalgebraic degreecompletely integrally closedNoetherian
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 162 - 164
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Bourbaki, N., Elements of Mathematics, Commutative Algebra, Addison Wesley, 1972.Google Scholar
2. Gilmer, R., A Note on the quotient field of the domain D[[X]], Proc. Amer. Math. Soc. 18(1967), 1138–1140.Google Scholar
3. Nagata, M., Local Rings, Interscience Publishers, 1962.Google Scholar
4. Ohm, J., Some counterexamples related to integral closure in D[[X]], Trans. Amer. Math. Soc. 122(1966), 321–333.Google Scholar
5. Sheldon, P. B., How changing D[[X]] changes its quotient field, Trans. Amer. Math. Soc. 159(1971), 223– 244.Google Scholar
6. Zariski, O. and Samuel, P., Commutative algebra, Vol. I, Van Nostrand, New York, 1958.Google Scholar