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Proof: By Induction

(related to Proposition: Criterions for Equality of Principal Ideals)

In the following proof, (R, + ,\cdot) is an integral domain.

"\Rightarrow"

"\Leftarrow"

If (a)=(0) then a\sim 0. Therefore, there exist b,c\in R with ab=0 and c0=a. In particular, a=0.


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