This has been bugging me for a while any help would be appreciated.
The second bullet point from here says:
Let A be a non-associative unital algebra with finite dimension, then it's possible to find a case (over R) where A has no zero divisors, but there exists a non-zero element in A that has no inverse (i.e. nonzero x, where xa = ax = 1).
Let A be a non-associative (although power-associative) unital algebra with finite dimension Then if A has no divisors implies every nonzero element in A has an inverse (particularly looking at the proof by Robert Lewis).
Is there a contradiction somewhere, or am I overlooking a use of associativity or technicality?