  In the framework of idempotent mathematics, analogs of the classical kernel
theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of
nuclear spaces (in the sense of A. Grothendieck) are discussed. The so-called
algebraic approach is used. This means that the basic concepts and results
(including those of "topological" nature) are simulated in purely algebraic
terms.
