Commuting U-Operators and Nondegenerate Imbeddings of Jordan Systems
Over an arbitrary ring of scalars, we build a Jordan
algebra J having two elements whose U-operators do not commute. This
shows that nondegeneracy is a necessary condition in the main theorem
of "Commuting U-Operators in Jordan Algebras" by J. A Anquela, T.
Cortes, and H. P. Petersson (Number 323 on this server). As a
consequence, we obtain examples of Jordan systems over arbitrary
rings of scalars that cannot be imbedded in nondegenerate systems.
J. A. Anquela < anque@orion.ciencias.uniovi.es >
T. Cortés < cortes@orion.ciencias.uniovi.es >
I. Shestakov < shestak@ime.usp.br >