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Proceedings of the American Mathematical Society

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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
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.


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  • [1] Clifton E. Corzatt, A large algebraically closed field, Proceedings of the 1972 Number Theory Conference (Univ. Colorado, Boulder, Colo.), Univ. Colorado, Boulder, Colo., 1972, pp. 53–55. MR 0396394
  • [2] Clifton Corzatt and Kenneth B. Stolarsky, Sequences generated by rational operations, Proceedings of the 1972 Number Theory Conference (Univ. Colorado, Boulder, Colo.), Univ. Colorado, Boulder, Colo., 1972, pp. 228–232. MR 0396393

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Additional Information

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