I am looking for an example of a semigroup wher the right inverse and right identity holds but it is not a group.
Is there an example of such a semigroup- i was not able to prove that if the above condiion holds then it is a group..
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A semigroup in which there is a right identity and every element has a right inverse is necessarily a group, so no such examples exist. See for example, here. – Arturo Magidin Mar 19 '22 at 05:49