is such a ring. Take the non-trivial automorphism of and extend it to an automorphism . The restriction of the latter automorphism to gives a non-trivial injection.
Notice that the image of by this automorphism cannot be , since there are no non-trivial automorphisms of .
The Noriega Book 
Notice that the image of
by this automorphism cannot be 
, since there are no non-trivial automorphisms of 
.
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Easier solution, proposed by Iván: consider the maps
given by 
and 
.
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