Unequal Left/Right Identity

• Oct 6th 2010, 06:24 PM
matt.qmar
Unequal Left/Right Identity
Hello,

I'm trying to find an example of any set S with a binary operation $\ast$ (meaning that it's closed) where there is a left identity that is NOT a right identity

So, for some $a,x \in S,$
$a \ast x = a$, but $x \ast a$ NOT $= a$

Thanks!
• Oct 6th 2010, 07:35 PM
undefined
Quote:

Originally Posted by matt.qmar
Hello,

I'm trying to find an example of any set S with a binary operation $\ast$ (meaning that it's closed) where there is a left identity that is NOT a right identity

So, for some $a,x \in S,$
$a \ast x = a$, but $x \ast a$ NOT $= a$

Thanks!

If you play around with a Cayley table for a set with two elements, you should find one pretty quickly.