  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
$\nu$-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.
