Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach

In the framework of idempotent mathematics, some analogs for the well-known kernel theorems of L. Schwartz and A. Grothendieck are examined. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are described. An algebraic approach is used, so topological concepts and results are simulated by means of algebraic tools.