Algebra
《Algebra》 · 第 434 页 · Section IX.3「Semisimple Rings」，Definition 3.1
A ring $R$ is said to be a subdirect product of the family of rings $\{R_i\mid i\in I\}$ if $R$ is a subring of the direct product $\prod_{i\in I}R_i$ such that $\pi_k(R)=R_k$ for every $k\in I$, where $\pi_k\colon\prod_{i\in I}R_i\to R_k$ is the canonical epimorphism.