page1881 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
Given a homomorphism `phi : A rightarrow B`, we define an equivalence
relation ~ on A by:
`x ~ y Leftrightarrow phi(x) = phi(y)`
`Rightarrow x - y in ker(phi)`.
We can write that y = x + (y - x) = x + z ,
where z = y - x.
Can we now conclude that `y - x in ker (phi) Rightarrow
y in x + ker (phi)`
?
