What do you call the element aside from the identity element which when a binary operation is applied to itself the product would be the identity element? example,

```
e * e = e <-- identity element
a * a = e <-- what do you call element a?
```

I have been searching for the term most appropriate for it but it seems that it doesn't have one.

If you do know what it is called, please tell me and please give me a link where i can read more about it. Thanks in advance!

## Comments

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TopNewestIdempotent – Calvin Lin Staff · 2 years, 3 months ago

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– Israel Sapnu Jr. · 2 years, 3 months ago

isn't it idempotent if a * a = a? i think the identity element for any group is idempotent, but what do you call element a if a * a = the identity element.Log in to reply

Self inverse – Calvin Lin Staff · 2 years, 3 months ago

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– Israel Sapnu Jr. · 2 years, 3 months ago

is there any special name for it?Log in to reply