/sci/ - Science & Math

Anonymous Tue Sep 12 07:51:23 2017 No.9163742 [View]
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[math]0 \longrightarrow M \overset{\varphi}\longrightarrow N \longrightarrow \mathrm{coker} \, \varphi \longrightarrow 0[/math]
I have this short exact sequence of modules and I'm reading a proof of the sequence being split iff [math]\varphi[/math] has a left inverse.
I might be retarded, but can someone explain how [math]\mathrm{ker} ~\psi[/math] got involved here? Is it isomorphic to [math]\mathrm{coker} ~ \varphi[/math]?

Anonymous Mon Sep 11 12:01:41 2017 No.9162157 [View]
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>>9148411
[math]0 \longrightarrow M \overset{\varphi}\longrightarrow N \longrightarrow \mathrm{coker} \, \varphi \longrightarrow 0[/math]
I have this exact sequence of modules and I'm reading a proof of the sequence being split iff [math]\varphi[/math] has a left inverse.
I might be retarded, but can someone explain how [math]\ker \psi[/math] got involved here? Is it isomorphic to [math]\mathrm{coker} \, \varphi[/math]?

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/sci/ - Science & Math

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