I apologize for this not being a more specific question. I am just wondering what conditions are "necessary" for the Chinese Remainder Theorem to hold true. I know that we need a surjective homomorphism, and I'm wondering if this is possible to find or not if we have a commutative ring without unity, or if $R \neq I + J$ for two ideals $I$ and $J?$
2026-04-01 04:38:47.1775018327
Can the Chinese Remainder Theorem be proved for a commutative ring without unity? Or if $I+J \neq R$?
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