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  "body": "\n## Definition\n\nLet $R$ and $S$ be [[rings|0894J980RK]].\nA ring isomorphism from $R$ to $S$ is a [[ring homomorphism|0GGE0Z0JQ1]] $f \\colon R \\to S$ that is bijective.\nThe rings $R$ and $S$ are isomorphic, written $R \\cong S$, if there is a ring isomorphism from $R$ to $S$.\n\n## Remarks\n\nThe inverse map of a ring isomorphism is again a ring homomorphism.\nA ring isomorphism from $R$ to $R$ is an automorphism of $R$.\nComplex conjugation is an automorphism of $\\mathbb{C}$.\n\n## Explanations\n\n### L1 human\n\nTwo isomorphic rings are the same ring with other names for the elements.\nThe isomorphism is the dictionary between the names.\n",
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