Abstract:

The properties of the solution configuration of valuation algebra over a totally ordered semiring were discussed. Furthermore, the concept of preserving the solution  configuration of valuation algebra over a totally ordered semiring was given. With the help of the properties of the solution configuration, the question of the transfer function f preserving solution  configuration was studied. It is concluded that the transfer function f preserves solution configuration if f is a semiring homomorphism.

Key words: valuation algebra, semiring, solution configuration, transfer function