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Apr 25, 2020 at 1:37 comment added LSpice @RichardStanley, could it be a difference of terminology (like which ones are right cosets, where one has to decide whether the representative or the group action is on the right)? I'd call a right identity of $R$ an element $i$ that satisfies $x i = x$ for all $x \in R$, in which sense it seems that $a$ and $b$ are both right identities here.
May 1, 2011 at 16:15 history edited Qiaochu Yuan CC BY-SA 3.0
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May 1, 2011 at 15:38 comment added Richard Stanley Not that it matters, but doesn't your example have two left identities, not two right identities?
May 1, 2011 at 15:35 history edited Qiaochu Yuan CC BY-SA 3.0
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May 1, 2011 at 14:32 history answered Qiaochu Yuan CC BY-SA 3.0