MHB Split Epimorphisms .... Bland Proposition 3.2.4 ....

[Math Amateur]

I am reading Paul E. Bland's book "Rings and Their Modules" ...

Currently I am focused on Section 3.2 Exact Sequences in [FONT=MathJax_Main]Mod[FONT=MathJax_Math]R ... ...

I need some help in order to fully understand Proposition 3.2.4 ...

Proposition 3.2.4 reads as follows:
View attachment 8076
Can someone please explain exactly how Proposition 3.2.3 establishes Proposition 3.2.4 ...
Help will be much appreciated ...

Peter

 

[castor28]

Hi Peter,

This is a consequence of the remark after definition 3.2.2.

In the case of proposition 3.2.4, $g':M_2\to M$ is a split monomorphism with splitting map $g$, and you can use proposition 3.2.3.

 

[Math Amateur]

Hi Peter,

This is a consequence of the remark after definition 3.2.2.

In the case of proposition 3.2.4, $g':M_2\to M$ is a split monomorphism with splitting map $g$, and you can use proposition 3.2.3.

Thanks for the help, castor28 ...

Peter