Journal or Book Title
Comptes Rendus Mathématique
In the free communtative power associative algebras, we show that the Jordan associator (aa, b, a) does not square to zero and is not in the left, right, or middle nucleus. We show the same properties for (aa, a, b). These and some other questions were answered by constructing a counterexample. We contrast this approach with the characteristic function type proof that was used to show that in a right alternative algebra, the cube of the alternator need not be zero.
Royal Society of Canada
Hentzel, Irvin Roy and Jacobs, David P., "Jordan and right alternative counterexamples" (1989). Mathematics Publications. 240.