An eigenvector existence theorem in idempotent analysis

In this paper, we prove an eigenvector existence theorem for linear operators on abstract idempotent spaces in the framework of the algebraic apporoach. Earlier, an algebraic version of a similar statement was known only for operators in free finite-dimensional semimodules. The corresponding result for compact operations in semimodules of real continuous functions is known in the case of topological semimodules.