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Are there any rings that have a left identity but do not have a right identity?

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    $\begingroup$ if $e$ is a unique left identity, this is impossible but you can construct examples that have more than one left identity. $\endgroup$ – Andres Mejia Mar 27 '18 at 16:34
  • $\begingroup$ @AndresMejia so in your second linked example, say we take the same setup but instead have the condition that a+b=1 must hold. Would this then satisfy left identity but not right identity? $\endgroup$ – tdashrom Mar 27 '18 at 16:44
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    $\begingroup$ You can fix that immediately by dualizing the example (AKA) take the transpose. $\endgroup$ – Andres Mejia Mar 27 '18 at 18:08

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