| Abstract: In this paper, a semimodule RM over a general semiring(R,+,) (where (R,+) is a commutative semigroup and (R,) is a semigroup with the multiplication distributing over addition from either side ) is introduced . And we introduce the star element with absorbing property for the operations " + ", " o" of a semimodule M . Furthermore , we define a star semimodule and a star subsemimodule (a subset of M with absorbing property for the operations "+ ", "o ").Based on this ,we introduce star congruences and discuss the homomorphic theorem and some properties of star subsemimodules of M about semimodule homomorphisms . In the end , we construct the free star semimodule over a semiring with a unit.
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