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# Prove that if k is a eld and f (x), g (x) k [x] are relatively prime, then k [x]/(f (x)g (x)) k [x]/(f (x)) k [x]/(g (x)) = 1

Hello,

I'm trying to show a specific property using the chinese remainder thm. See attachment.
Prove that if k is a ﬁeld and f ( x ) ,g ( x ) k [ x ] are relatively prime, then k [ x ] / ( f ( x ) g ( x )) = k [ x ] / ( f ( x )) × k [ x ] / ( g ( x )) 1

Dear student, Pleasefind... View the full answer

Chinese Remainder Theorem
This theorem was first used by Chinese Mathematician Sun Tzu in third
century AD. This theorem states about simultaneous congruencies. It
says that suppose there are...

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