English

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 17th17^{th} 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

R2 v1 2026-06-23T03:58:54.724Z