2013/07/28 by Tal Perri, Perri, Tal
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.AG #math.RA
paper · pdf · doi:10.48550/arxiv.1307.7336
21 pages
arxiv created 2013/07/28 · openalex publication_date 2013/07/28 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce a canonical method of constructing simple uniform semifield extensions of uniform layered semifields introduced by Izhakian Knebusch and Rowen in the paper 'Layered tropical mathematics'. Our construction includes a decomposition of a uniform extension of a uniformly layered (uniform) semifield to the bipotent semifield extension of its ν-values semifield and a cancellative semifields extension of its layers (sorting) semifield. We give a characterization of these two types of semifields extensions in the first two sections of the paper. The third section glues the pieces together to form a theory for a uniform extension of a uniformly layered semifield.