A Theory Of The Endomorphism Ring Of The Module With Direct Summands Of Free Submodule

In this paper we investigate the endomorphism rings of the modules with the form as M=Ru⊕N,where R is the ring with identity,the summand Ru is the free submodule of M.Through investigation we find that one right ideal M°of the endomorphism ringΩ= End(_RM) could outspread to a module which is Semi-linear isomorphic to M,and the endomorphism ring of the module is alsoΩ,and get some theories related to the endomorphism rings.Then we can replace some work on M with on M°composed completely of linear transformations.These results provide an effective method for the investigation on the endomorphism rings of the modules with free summands.