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MHB

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I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some further help in order to fully understand the proof of Lemma 4.3.12 ... ...

Lemma 4.3.12 reads as follows:View attachment 8316My question is as follows:

In the Lemma R is a PID ... where in the proof are the special properties of a PID used/needed ... it seems to me that the argument of the proof would hold valid for an ordinary commutative ring with identity ...

Can someone please point out the points in the proof where the special properties of a PID are needed ...

Peter

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It may help MHB

readers of the above post to have access to Bland's definition of a primitive element ... so I am providing the same as follows:View attachment 8317

Hope that helps ...

Peter