Affine Nash groups over real closed fields
Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 577-585.

We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-points of some algebraic group H defined over R. In the case when R = ℝ, this result was claimed in [5], but a mistake in the proof was recently found, and the new proof we obtained has the advantage of being valid over an arbitrary real closed field. We also extend the result to not necessarily connected affine Nash groups over arbitrary real closed fields.

Published online:
DOI: 10.1142/S179374421100045X
Ehud Hrushovski 1; Anand Pillay 1

1
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Ehud Hrushovski; Anand Pillay. Affine Nash groups over real closed fields. Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 577-585. doi : 10.1142/S179374421100045X. https://cml.centre-mersenne.org/articles/10.1142/S179374421100045X/

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