Nullstellens\"atze and Applications
Commutative Algebra
2022-02-25 v2
Abstract
In this expository paper, we present simple proofs of the Classical, Real, Projective and Combinatorial Nullstellens\"atze. Several applications are also presented such as a classical theorem of Stickelberger for solutions of polynomial equations in terms of eigenvalues of commuting operators, construction of a principal ideal domain which is not Euclidean, Hilbert's problem, the Borsuk-Ulam theorem in topology and solutions of the conjectures of Dyson, Erd\"{o}s and Heilbronn.
Keywords
Cite
@article{arxiv.1809.02818,
title = {Nullstellens\"atze and Applications},
author = {Kriti Goel and Dilip P. Patil and Jugal Verma},
journal= {arXiv preprint arXiv:1809.02818},
year = {2022}
}
Comments
39 pages