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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0360546-6
PII: S 0002-9939(1974)0360546-6
Keywords: Algebraic number, algebraically closed field
Article copyright: © Copyright 1974 American Mathematical Society