I have trouble finding a definition for the associativity from operators with arity higher than 2. At first I tried to think how it would be done for an operator with arity=3, and then generalize it, but I am not sure how many elements I need, if just adding one more, or adding n-1 elements. Could someone help me with a definition or explanation? Thak you!
So the reason I am looking into this is because I want to show that a universal algebra (G,p) from type (3), with $$ p(x,y,z):= x\cdot y^{-1}\cdot z $$ is a Group. That means I have to express the axioms (associativity, neutral element and inverse elemet) using the operation $p$.