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 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 , where is an algebraic number.

**[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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DOI:
https://doi.org/10.1090/S0002-9939-1974-0360546-6

Keywords:
Algebraic number,
algebraically closed field

Article copyright:
© Copyright 1974
American Mathematical Society