page1884 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
Let us show that `x + ker (phi) sube [x]`.
Given a homomrphism `phi: A rightarrow B`, we define
an equivalence relation ~ on A by: `x ~ y Leftrightarrow phi(x) = phi(y)`.
Let `y in x + ker(phi)`. Then `phi(y) =`
`phi(x + z) = phi(x) + phi(z) = phi(x) Leftrightarrow` y is in
the same equivalence class as x
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