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arXiv · 1809.02818

Nullstellens\"atze and Applications

Kriti Goel·Dilip P. Patil·Jugal Verma
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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 $17^{th}$ problem, the Borsuk-Ulam theorem in topology and solutions of the conjectures of Dyson, Erd\"{o}s and Heilbronn.

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Kriti Goel, Dilip P. Patil, Jugal Verma. 2018-09-08. Nullstellens\"atze and Applications. https://arxiv.org/abs/1809.02818

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