Predicable R-semimodule with some properties

In this paper divided into two parts, related to the concept of projective semimodule we tried to clarify the general concepts of this common topic and other concepts related to it.The first part includes the definition of preradicale semimodule and the properties related to it, and we gave examples on the subject similar to what is found in the module and expanded on the definitions, examples, proofs and results obtained by solving the problems arising from this expansion in the scope of work from the concept of the projective module to the projective semimodule. The second part we put some illustrative examples on the subject of preradicale semimodule and referred to the concept of Jacobson and radical because of its importance in understanding and solving the issues related to it and we put forward several expanded definitions than they were in the subject of the module and the basic results that we needed to prove some properties. Secondly, we studied the Socle radical of semimodule and proved some properties.