Schur–Brauer version of van der Waerden's theorem for semimodules
Let G=B1∪⋯∪BqG=B_1\cup\dotsm\cup B_qG=B1∪⋯∪Bq be a finite partition of a semimodule (G,+)(G,\pmb{+})(G,+) over a semiring (R,+,⋅)(R,+,\cdot)(R,+,⋅). For a subset F⊆RF\subseteq RF⊆R, write Fb={fb:f∈F}Fb=\{fb:f\in F\}Fb={fb:f∈F}. Schur–Brauer…
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