The Homomorphisms of Distributive Semimodules

Many researchers discussed distributive modules and their properties. In this work, the distributive property will be studied over semimodules. Some of the results obtained in homomorphisms of distributive modules are generalized. Some conditions were needed like concept subtractive, i-regular, k-regular, and k-cyclic, to get good results. The relationship between the distributive semimodule over the local semiring and the hollow semimodule was obtained, and the relationship between the distributive semimodule and the homomorphisms distributed over the intersection process or the inverse image distributed over the addition.