When we talk about an abstract binary operation *:SxS --> S(adsbygoogle = window.adsbygoogle || []).push({});

We say that an identity element "e" exists when e * x = x * e = x, (x; e belong to S)

Now my questions:

1) If the operation is not commutative, does not this imply no identity? since e * x != x * e necessarily?

2) Does e * x = x imply x * e = x? And if one side is true, can we still say that * has an identity restricted to one side?

3) Is there cases where not all x's of the set S have the same identity wrt operation *?

These questions are regardless of any kind of algebraic structure.

Thanks.

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# Algebraic Operation Identity

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