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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

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