Hilbert’s Nullstellensatz
https://doi.org/10.26907/2949-3919.2024.1.3-15
Abstract
Hilbert’s Nullstellensatz proved by him in 1890 is one of the basic results in modern algebraic geometry. We give various statements and proofs of this theorem all of which are used in algebraic geometry. All notions and facts outside the basic algebra course are explained in the paper.
About the Authors
B. M. Bekker
St.Petersburg State University
Russian Federation
Russian Federation
Boris Meerovich Bekker
7–9 Universitetskaya Embankment, St. Petersburg 199034
S. V. Vostokov
St.Petersburg State University
Russian Federation
Russian Federation
Sergei Vladimirovich Vostokov
7–9 Universitetskaya Embankment, St. Petersburg 199034
R. P. Vostokova
St.Petersburg State University
Russian Federation
Russian Federation
Regina Petrovna Vostokova
7–9 Universitetskaya Embankment, St. Petersburg 199034
References
1. I.R. Shafarevich, Basic Algebraic Geometry, 2 volumes, Springer-Verlag, Heidenberg, 2013.
2. E. Arrondo, Another elementary proof of the Nullstellensatz, Amer. Math. Monthly 113 (2), 169–171 (2006). DOI: https://doi.org/10.1080/00029890.2006.11920292
3. S. Lang, Introduction to algebraic geometry, Interscience Publ., N.Y., 1958.
4. D. Mumford, Algebraic Geometry I: Complex Projective Varieties, Springer-Verlag, Berlin, 1976.
5. D. Perrin, Algebraic geometry, Springer-Verlag, London, 2008.
Review
For citations:
Bekker B.M., Vostokov S.V., Vostokova R.P. Hilbert’s Nullstellensatz. Mathematics and Theoretical Computer Science. 2024;2(1):3-15. (In Russ.) https://doi.org/10.26907/2949-3919.2024.1.3-15
Views:
427
Email this article 