Abstract
We explain how the construction of the real numbers using quasimorphisms can be transformed into a general method to construct the completion of a field with respect to an absolute value.
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References
N. A’Campo, “A natrural construction for the real numbers,” arxiv:math/0301015, (2003).
R. D. Arthan, “The Eudoxus real numbers,” arXiv:math/0405454, (2004).
E. Bloch, The Real Numbers and Real Analysis (Springer, New York, 2011).
T. Grundhöfer, “Describing the real numbers in terms of integers,” Arch. Math. (Basel) 85, 79–81 (2005).
J. Neukirch, Algebraic Number Theory (Springer, Berlin, 1999).
G. Pilz, Near-Rings (North-Holland Publishing Company, Amsterdam, 1977).
R. Street, “An efficient construction of real numbers,” Austral. Math. Soc. Gaz. 12, 57–58 (1985).
I. Weiss, “Survey article: The real numbers–a survey of constructions,” Rocky Mountain J. Math. 45, 737–
Acknowledgements
We thank an anonymous referee for pointing us to the notion of near-rings.
Funding
The research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 338540207.
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Kionke, S. Constructing the Completion of a Field Using Quasimorphisms. P-Adic Num Ultrametr Anal Appl 11, 335–337 (2019). https://doi.org/10.1134/S2070046619040083
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DOI: https://doi.org/10.1134/S2070046619040083