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I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums.
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:
https://www.physicsforums.com/attachments/2427
As can be seen in the above text, the first line of the proof reads as follows:
-----------------------------------------------------------------------------
Proof. Let N be an R-Module and suppose that, for each $$\alpha \in \Delta, \ \ f_\alpha : \ N \to M_\alpha $$ is an R-linear mapping.
... ... ... etc. etc.-----------------------------------------------------------------------------
My question is as follows:
How do we know such a family of module homomorphisms or R-linear mappings $$ f_\alpha $$ from $$ N $$ to $$ M_\alpha $$ exist?
... ... or is the point that if they do not exist, then the direct product does not exist?
Hope someone can help.
Peter
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:
https://www.physicsforums.com/attachments/2427
As can be seen in the above text, the first line of the proof reads as follows:
-----------------------------------------------------------------------------
Proof. Let N be an R-Module and suppose that, for each $$\alpha \in \Delta, \ \ f_\alpha : \ N \to M_\alpha $$ is an R-linear mapping.
... ... ... etc. etc.-----------------------------------------------------------------------------
My question is as follows:
How do we know such a family of module homomorphisms or R-linear mappings $$ f_\alpha $$ from $$ N $$ to $$ M_\alpha $$ exist?
... ... or is the point that if they do not exist, then the direct product does not exist?
Hope someone can help.
Peter
Last edited: