Ring with left identity but no right identity?

Asked Mar 27 '18 at 16:27

Active Mar 27 '18 at 17:50

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

edited Mar 27 '18 at 17:50

asked Mar 27 '18 at 16:27

tdashrom

2

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
1

You can fix that immediately by dualizing the example (AKA) take the transpose. – Andres Mejia Mar 27 '18 at 18:08

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