The Characterization Of Generating And Cogenerating In The Category Of Semimodules

In this paper , the auther defines the generating and cogenerating in the category of semimodules and generalizes some results that the generating and cogenerating are "Transitive". The last result gives a very useful characterization of Gen(U) and Cog(U).In the next chapter, the author defines and studies the trace and reject in the category of semimodules , the last result tells us whether or not semimodule RM is a generator, its trace in R is a measure of how close it comes to being one .In chapter 4 , we study the characterization of Horn functor in the category of semimodules and and generalizes some results. Finally , we get some results about the generator of semimodules.