Is there an example of a nonzero ring $R$ such that its proper subrings have identity but $R$ has no identity ? or even is it possible that proper nonzero subrings of $R$ have the same identity but $R$ has no identity element ??
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closed as off topic by S. Carnahan♦ Feb 9 '13 at 7:53Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 

