A General Version of the Nullstellensatz for Arbitrary Fields

A General Version of the Nullstellensatz for Arbitrary Fields

We prove a general version of Bezout’s form of the Nullstellensatz for arbitrary fields. The corresponding sufficient and necessary condition only involves the local existence of multi-valued roots for each of the polynomials belonging to the ideal in consideration. Finally, this version implies the...

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2019-06, Vol.17 (1), p.556-558
Hauptverfasser: Gallego, Edisson, C., Juan D. Vélez, Gómez-Ramírez, Danny A. J.
Format: Artikel
Sprache:eng
Schlagworte:
Algebraically closed fields
Mathematical analysis
Polynomial roots
Polynomials
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Zusammenfassung:We prove a general version of Bezout’s form of the Nullstellensatz for arbitrary fields. The corresponding sufficient and necessary condition only involves the local existence of multi-valued roots for each of the polynomials belonging to the ideal in consideration. Finally, this version implies the standard Nullstellensatz when the coefficient field is algebraically closed.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0046