Linear functionals on idempotent spaces: an algebraic approach
  In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions of certain basic results of linear functional analysis, including the theorem on the general form of a linear functional and the Hahn-Banach and Riesz-Fischer theorems. 
Grigori Litvinov, Victor Maslov, Grigori Shpiz