Let \(\tilde{K}\) be an algebraically closed field and consider the ideal I generated by polynomials f1,…,f m in \(\tilde{K}[X_{1},\ldots,X_{n}]\) . The Hilbert Nullstellensatz asserts that if I is not the whole ring, then f1,…,f m have a common \(\tilde{K}\) -zero. Conversely, this property is a suficient condition for a field K to be algebraically closed.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Pseudo Algebraically Closed Fields. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77270-5_11
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DOI: https://doi.org/10.1007/978-3-540-77270-5_11
Publisher Name: Springer, Berlin, Heidelberg
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