Notes on Direct Products of Group and the Direct Sums of Rings

Abstract

The group and ring are one of the main contents of algebraic research. As the important tool of natural science research, they have a wide range of applications. In this paper, the direct products of their important properties for a given finite group have been studied. When given a few groups are abelian groups, their direct product naturally becomes the direct sums of commutative rings. So this paper also studied the direct sums of ring. Finally, the important properties of direct product and direct sums under the sense of isomorphism are obtained.