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I am currently focused on Chapter 2: Rings ...

I need help with an aspect of the proof of Corollary 2.4 ... ...

Corollary 2.4 and its proof read as follows:View attachment 7933

In the above proof of Corollary 2.4 we read the following:

" ... ... If \(\displaystyle \text{Ker} (f) = \{ 0 \}\) then \(\displaystyle f\) is injective ... ... "

Can someone please explain exactly how/why \(\displaystyle \text{Ker} (f) = \{ 0 \}\) implies that \(\displaystyle f\) is injective ... ?

Help will be appreciated ...

Peter