Tropical Cramer Determinants Revisited

We dedicate this paper to the memory of our friend and colleague Grigory L. Litvinov. Abstract. We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are en-riched with an information of multiplicity, sign, or argument. We obtain exis-tence or uniqueness results, which extend or refine earlier results of Gondra