Tropical Algebraic Sets, Ideals and An Algebraic Nullstellensatz

Details Tropical Algebraic Sets, Ideals and An Algebraic Nullstellensatz Tropical Algebraic Sets, Ideals and An Algebraic Nullstellensatz

2005-11-02

arxiv.org/abs/math/0511059v3

International Journal of Algebra and Computation, 18(6):1067-1098, 2008

Mathematics

Commutative Algebra

21 pages, 2 figures

Scientific paper

This paper introduces the foundations of the polynomial algebra and basic structures for algebraic geometry over the extended tropical semiring. Our development, which includes the tropical version for the fundamental theorem of algebra, leads to the reduced polynomial semiring -- a structure that provides a basis for developing a tropical analogue to the classical theory of commutative algebra. The use of the new notion of tropical algebraic com-sets, built upon the complements of tropical algebraic sets, eventually yields the tropical algebraic Nullstellensatz.

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