Suppose we have a set $S$ with a binary operation $*$ such that for all $x,y,z$ $\in$ $S$, $(x*y)*z=(x*z)*y$. For example, subtraction on the integers and also the real numbers has this property. Is there a standard name for this property in the mathematical literature?
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Not sure if there is a name for this, but it's a combination of associativity and commutativity. So if you have those properties, you have the one you want – Andrei Sep 01 '20 at 15:54
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1Exponentiation has the property also. – Somos Sep 01 '20 at 16:03
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1This amounts to saying all of the operators $f_y : x \mapsto x * y$ commute. – Jair Taylor Sep 01 '20 at 16:06