Zajaczkowska, Magdalena Anna (2018) Tropical ideals with Hilbert function two. PhD thesis, University of Warwick.

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Abstract

We study tropical ideals with Hilbert function two, i.e., homogeneous ideals in the tropical polynomial semiring such that each degree has the underlying structure of a valuated matroid of rank two. We classify all such ideals when the matroid is over the field ꓐ. We discuss the realizability of such ideals when they are in two and three variables. We also give necessary conditions for a sequence of valuated matroids over R to correspond to a tropical ideal in two variables

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Characteristic functions, Algebra, Algebras, Linear
Official Date:	March 2018
Dates:	Date Event March 2018 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Maclagan, Diane,1974-
Extent:	v, 58 leaves
Language:	eng

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