Field extension
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Revision 310
7/7/2026, 3:03:27 PM · Ancient Tree
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A field extension is a [[homomorphism of fields|homomorphism of fields]] $K\rightarrow L$. It is denoted as $K\subseteq L$.2
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##### Remarks 4
- Any homomorphism of fields is injective, so $K$ can be identified with its [[Image of a map|image]] in $L$; we simply regard $K$ as a [[Subfield|subfield]] of $L$.Revision 301
7/7/2026, 2:49:32 PM · Ancient Tree
Concept edited
Compare with revision 2982 changed lines
1
A field extension is a [[homomorphism of fields|homomorphism of fields]] $K\rightarrow L$. It is denoted as $K\subseteq L$.2
3
##### Remarks 4
- Any homomorphism of fields is injective, so $K$ can be identified with its image in $L$; we simply regard $K$ as a subfield of $L$.4
- Any homomorphism of fields is injective, so $K$ can be identified with its [[Image of a map|image]] in $L$; we simply regard $K$ as a [[Subfield|subfield]] of $L$.Revision 298
7/7/2026, 2:46:54 PM · Ancient Tree
Concept created
A field extension is a [[homomorphism of fields|homomorphism of fields]] $K\rightarrow L$. It is denoted as $K\subseteq L$. ##### Remarks - Any homomorphism of fields is injective, so $K$ can be identified with its image in $L$; we simply regard $K$ as a subfield of $L$.