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G-2013-67

Strong Independence and Injectivity in Tropical Modules

BibTeX reference

Tropical algebra is the study of algebraic structures (tropical maps, idempotent semimodules, etc), constructed over the semifield R_=R{} with the max operator (resp. usual addition) as 1st (resp.2nd) composition law. After showing first that the concept of injectivity module of a tropical map A:R_mR_n introduced in [Wagneur, E., The Whitney embedding theorem for tropical torsion modules. Classification of tropical modules, Linear Algebra and its Applications, 435, 2011, 1786-1795] fails to be sufficient for the characterisation of ImA, we introduce the concept of injectivity domain, and study some of the properties of a matrix ΓA whose columns are given by the saturation of the equivalence class (modulo A) of the canonical basis of R_m. Numerous examples are provided.

, 12 pages

Publication

Strong independence and injectivity in tropical modules
G Litvinov, VP Maslov, AG Kushner and SN Sergeev (eds.), Contemporary Mathematics, 616, American Mathematical Society, 291–300, 2014 BibTeX reference