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'field homomorphism'
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| Title of object: |
field homomorphism |
| Canonical Name: |
FieldHomomorphism |
| Type: |
Definition |
| Created on: |
2003-08-29 16:47:32 |
| Modified on: |
2003-08-29 16:47:32 |
| Classification: |
msc:12E99 |
| Keywords: |
field, map |
| Defines: |
field homomorphism, field isomorphism |
Revision comment (for changes between this and next version):
| Changes for correction #2501 ('injectivity'). |
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Content:
Let $F$ and $K$ be fields.
\begin{defn}
A {\em field homomorphism} is a function $\psi\colon F \longrightarrow K$ such that:
\begin{enumerate}
\item $\psi(a+b) = \psi(a)+\psi(b)$ for all $a,b \in F$
\item $\psi(a\cdot b) = \psi(a) \cdot \psi(b)$ for all $a,b \in F$
\item $\psi(1)=1,\quad \psi(0)=0$
\end{enumerate}
If $\psi$ is injective and surjective, then we say that $\psi$ is a \emph{field isomorphism}.
\end{defn} |
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