A large algebraically closed field
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- by Clifton E. Corzatt PDF
- Proc. Amer. Math. Soc. 46 (1974), 191-194 Request permission
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
- 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
- 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
Additional Information
- © Copyright 1974 American Mathematical Society
- 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