Generalization of Goursat's Theorem for Subrings of Direct Products of n Rings

Abstract

Bauer et al. describe Goursat’s theorem, representing the characteristics of subgroups of a direct product of two or more groups. In this paper, we expand into a ring structure that describes the characteristics of subrings of a direct product of rings. This research method is to analogize the evidence by Bauer et al. in the group for generalization. In our main results, every subring of the direct product of rings is determined by ring epimorphism between the ring and factor ring.
 Keywords: Goursat’s theorem, subrings, rings