I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums.(adsbygoogle = window.adsbygoogle || []).push({});

I have a question regarding the proof of Proposition 2.1.1

Proposition 2.1.1 and its proof (together with with a relevant preliminary definition) read as follows:

As can be seen in the above text, the first line of the proof reads as follows:

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Proof. Let N be an R-Module and suppose that, for each [itex]\alpha \in \Delta, \ \ f_\alpha : \ N \to M_\alpha [/itex] is an R-linear mapping.

... ... ... etc. etc.

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My question is as follows:

How do we know such a family of module homomorphisms or R-linear mappings [itex] f_\alpha [/itex] from [itex] N [/itex] to [itex] M_\alpha [/itex] exist?

... ... or is the point that if they do not exist, then the direct product does not exist?

Hope someone can help.

Peter

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# Direct Products of Modules - Bland - Proposition 2.1.1 and its proof

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