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Nullstellensätze and Applications

In this expository paper, we present simple proofs of the Classical, Real, Projective and Combinatorial Nullstellensätze. 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, Erdös and Heilbronn.