Ideals of polynomial semirings in tropical mathematics

Details Ideals of polynomial semirings in tropical mathematics Ideals of polynomial semirings in tropical mathematics

2011-11-27

arxiv.org/abs/1111.6253v1

Mathematics

Commutative Algebra

22 pages

Scientific paper

We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from layered varieties, for which we prove that every prime ideal is a consequence of finitely many binomials. We also obtain layered tropical versions of the classical Principal Ideal Theorem and Hilbert Basis Theorem.

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