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I am reading "Algebra: An Approach via Module Theory" by William A. Adkins and Steven H. Weintraub ...
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 $$\text{Ker} (f) = \{ 0 \}$$ then $$f$$ is injective ... ... "
Can someone please explain exactly how/why $$\text{Ker} (f) = \{ 0 \}$$ implies that $$f$$ is injective ... ?
Help will be appreciated ...
Peter
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 $$\text{Ker} (f) = \{ 0 \}$$ then $$f$$ is injective ... ... "
Can someone please explain exactly how/why $$\text{Ker} (f) = \{ 0 \}$$ implies that $$f$$ is injective ... ?
Help will be appreciated ...
Peter