I am reading Dummit and Foote, Chapter 10, Section 10.5, Exact Sequences - Projective, Injective and Flat Modules.(adsbygoogle = window.adsbygoogle || []).push({});

I need help with a minor step of D&F, Chapter 10, Theorem 28 on liftings of homomorphisms.

In the proof of the first part of the theorem (see image below) D&F make the following statement:

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Conversely, if F is in the image of [itex] \psi'[/itex] then [itex] F = \psi' (F') [/itex] for some [itex] F' \in Hom_R (D, L) [/itex] and so [itex] \phi ( F (d) )) = \phi ( \psi ( F' (d))) [/itex] for any [itex]d \in D[/itex]. ...

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My problem is that surely [itex] F = \psi' (F') [/itex] implies that [itex] \phi ( F (d) )) = \phi ( \psi' ( F' (d))) [/itex] and NOT [itex] \phi ( F (d) )) = \phi ( \psi ( F' (d))) [/itex]?

Hoping someone can help>

Theorem 28 and the first part of the proof read as follows:

Peter

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# Exact Sequences - Lifting Homomorphisms - D&F Ch 10 - Theorem 28

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