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  "body": "\n## Summary\n\nA field homomorphism is a map between two fields that respects addition, multiplication and the unit element.\nIt is a [[ring homomorphism|0VTH8KPCG2]] whose source and target are fields.\nEvery field homomorphism is injective, so it identifies the first field with a subfield of the second.\nThis is why field theory speaks of embeddings and of [[field extensions|0EQWVHF3W5]].\n\n## Explanations\n\n### L1 human\n\nA field homomorphism copies one field into another without breaking any computation.\nThe inclusion of the rational numbers into the real numbers is one.\nComplex conjugation $a + bi \\mapsto a - bi$ is a field homomorphism from $\\C$ to itself.\nSuch a map can never send a nonzero number to $0$, so it never merges two elements.\nThe [[definition|JBZMRZY4YF]] lists the conditions.\n",
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