Constructing a subring of the endomorphism ring of an additive group at first, this paper gets some results about the existence of the identity of the subring, and the relation between the direct summand of the additive group and the identity of the subring. 本文讨论了加法群的自同态环的一个子环,得到了关于这个子环的单位元的存在性及当单位元存在时与加法群的直和成分的关系等方面的一些结论。