Ivan Shishkin, Birch Grove

Field homomorphism

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Revision 1026

8/7/2026, 8:38:21 AM · Ancient Tree

Updated linked exercises

linked exercisesField homomorphisms from R\R to C\mathbb{C}None

Revision 1024

8/7/2026, 8:37:26 AM · Ancient Tree

Updated linked exercises

linked exercisesNoneField homomorphisms from R\R to C\mathbb{C}

Revision 1021

8/7/2026, 8:13:34 AM · Ancient Tree

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titleHomomorphism of fieldsField homomorphism
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1A homomorphism of fields is...
1Let $F$ and $F'$ be [[Field|fields]]. A function $\varphi:F \rightarrow F'$ is a field homomorphism if for all $a,b\in F$:
21. $\varphi(a+b)=\varphi(a)+\varphi(b)$
32. $\varphi(a\cdot b)=\varphi(a)\cdot\varphi(b)$
43. $\varphi(1)=1$
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7##### Remarks
8- This is the same definition as a [[ring homomorphism|ring homomorphism]], but between fields.

Revision 297

7/7/2026, 2:45:05 PM · Ancient Tree

Concept created

A homomorphism of fields is...