- #1
calvino
- 108
- 0
Chinese Remainder Theorem!
I'm pretty sure that the following is in fact the Chinese remainder Theorem:
If n= (m1)(m2)...(mk) [basically, product of m's (k of them)]
where each m is relatively prime in pairs, then there is an isomorphism from Zn to ( Zm1 X Zm2 X ... X Zmk). Zn is the integers modulo n.
All the proofs of the chinese remainder theorem I found searching online, are either the ones that focus on modulo, or focus more on ideals (and proving a certain mapping is an isomorphism). How do I go about proving the statement up there?
I'm pretty sure that the following is in fact the Chinese remainder Theorem:
If n= (m1)(m2)...(mk) [basically, product of m's (k of them)]
where each m is relatively prime in pairs, then there is an isomorphism from Zn to ( Zm1 X Zm2 X ... X Zmk). Zn is the integers modulo n.
All the proofs of the chinese remainder theorem I found searching online, are either the ones that focus on modulo, or focus more on ideals (and proving a certain mapping is an isomorphism). How do I go about proving the statement up there?