Chinese Remainder Theorem

Last updated January 27, 2022

For ideals

Theorem. If $I_1,\ddots,I_k$ are pairwise coprime ideals, then

1. $I_1\cap\cdots\cap I_k=I_1\cdot \dots \cdot I_k$
2. $\phi:A\to\prod_i A/I_i$ is surjective