Does commutativity imply associativity? I’m asking this because I was trying to think of structures that are commutative but non-associative but couldn’t come up with any. Are there any such examples?
NOTE: I wasn’t sure how to tag this so feel free to retag it.
Answer
Consider the operation (x,y)↦xy+1 on the integers.
Attribution
Source : Link , Question Author : Eugene , Answer Author : marlu
