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並前往https://mathoverflow.net/questions/31495/when-does-a-ring-surjection-imply-a-surjection-of-the-group-of-units

When does a ring surjection imply a surjection of the group of ...

If R is a local ring and S is its residue field then the map is onto, but that's too easy, isn't it? I don't think this is a trivial question at all!

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