Nullstellens\"atze and Applications
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 17th problem, the Borsuk-Ulam theorem in topology and solutions of the conjectures of Dyson, Erd\"os and Heilbronn.
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