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On euclidean rings of algebraic functions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 311)

Abstract

A large class of rings of algebraic functions are shown to be principal ideal domains but not Euclidean with respect to any possible algorithm.

Keywords

  • Riemann Surface
  • Finite Field
  • Function Field
  • Algebraic Function
  • Algebraic Extension

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was in part supported by a National Science Foundation Grant.

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References

  1. M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, New York 1966.

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  2. R. E. MacRae, On unique factorization in certain rings of algebraic functions, J. of Alg., 17(1971), 243–261.

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  3. P. Samuel, About Euclidean rings, J. of Alg., 19(1971), 282–301.

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  4. P. Samuel, Lectures on Old and New Results on Algebraic Curves, Tata Institue, Bombay, 1966.

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© 1973 Springer-Verlag

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MacRae, R.E. (1973). On euclidean rings of algebraic functions. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068927

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  • DOI: https://doi.org/10.1007/BFb0068927

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06140-3

  • Online ISBN: 978-3-540-38340-6

  • eBook Packages: Springer Book Archive