# Ring with left identity but no right identity?

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

• if $e$ is a unique left identity, this is impossible but you can construct examples that have more than one left identity. – Andres Mejia Mar 27 '18 at 16:34
• @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? – tdashrom Mar 27 '18 at 16:44
• You can fix that immediately by dualizing the example (AKA) take the transpose. – Andres Mejia Mar 27 '18 at 18:08