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I need help with another aspect of the proof of Proposition 2.1.1 ...

Proposition 2.1.1 and its proof read as follows:

https://www.physicsforums.com/attachments/8032In the above proof by Paul Bland we read the following:

" ... ... suppose that \(\displaystyle g \ : \ N \rightarrow \prod_\Delta M_\alpha\) is also an \(\displaystyle R\)-linear mapping such that \(\displaystyle \pi_\alpha g = f_\alpha\) for each \(\displaystyle \alpha \in \Delta\). If g(x) = ( x_\alpha ) ... ... "When Bland puts \(\displaystyle g(x) = ( x_\alpha )\) he seems to be specifying

__\(\displaystyle g\) and then proves \(\displaystyle f = g\) ... ... I thought he was proving that for__

**a particular**__such that \(\displaystyle \pi_\alpha g = f_\alpha\) we have \(\displaystyle f = g\) ... can someone please clarify ... ?Help will be much appreciated ... ...Peter__

**any g**======================================================================================The above post mentions but does not define \(\displaystyle f\) ... Bland's definition of \(\displaystyle f\) is as follows:

View attachment 8033

Hope that helps ...

Peter