Is the Proof in Dummit and Foote's Chinese Remainder Theorem Inductive?

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In summary, the conversation discusses a proof of the Chinese Remainder Theorem in Dummit and Foote, involving induction. The speaker is unsure if the induction hypothesis is used and wonders if the proof method can be considered induction.
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icantadd
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In Dummit and Foote on pages 265-266, a proof is given of the Chinese Remainder Theorem. They claim to proceed by induction, but I cannot see where the induction hypothesis is used.

It seems that they could proved the statement for k=2, and then reduced the statement for k>2 to k=2. Is this induction?

Thank you for your help.
 
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icantadd said:
In Dummit and Foote on pages 265-266, a proof is given of the Chinese Remainder Theorem. They claim to proceed by induction, but I cannot see where the induction hypothesis is used.

It seems that they could proved the statement for k=2, and then reduced the statement for k>2 to k=2. Is this induction?

Thank you for your help.

I don't have a definite answer, but my feeling is that if your proof for values of n greater than 2 is base upon a showing that it is dependent upon the validity of the case for n = 2 then it is a form of induction.
 

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