A two-liner

Is there a ring A such that there are two different ring injections \Bbb{R}\to A?

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A two-liner

2 thoughts on “A two-liner

  1. \Bbb{C} is such a ring. Take the non-trivial automorphism of \Bbb{Q}[\sqrt{2}]/\Bbb{Q} and extend it to an automorphism \Bbb{C}/\Bbb{Q}. The restriction of the latter automorphism to \Bbb{R} gives a non-trivial injection.

    Notice that the image of \Bbb{R} by this automorphism cannot be \Bbb{R}, since there are no non-trivial automorphisms of \Bbb{R}.

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