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A large algebraically closed field


Author: Clifton E. Corzatt
Journal: Proc. Amer. Math. Soc. 46 (1974), 191-194
MSC: Primary 12F99
DOI: https://doi.org/10.1090/S0002-9939-1974-0360546-6
MathSciNet review: 0360546
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Abstract: A sequence is called an R.R.S. sequence if, roughly speaking, it is generated by some member of a set of recurrence formulas over the field $ Q(i)$ which involves only rational operations. It is proved that the set of limits of all convergent R.R.S. sequences forms a countable algebraically closed field. Moreover, the field is shown to contain all numbers of the form $ {e^\alpha }$, where $ \alpha $ is an algebraic number.


References [Enhancements On Off] (What's this?)

  • [1] C. Corzatt, A large algebraically closed field, Proc. 1972 Number Theory Conference, Boulder, Colorado, pp. 53-55. MR 0396394 (53:261)
  • [2] C. Corzatt and K. B. Stolarsky, Sequences generated by rational operations, Proc. 1972 Number Theory Conference, Boulder, Colorado, pp. 228-232. MR 0396393 (53:260)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0360546-6
Keywords: Algebraic number, algebraically closed field
Article copyright: © Copyright 1974 American Mathematical Society

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