Fitting decomposition in Jordan systems (Q805729)

The well known Fitting decomposition of an endomorphism f of a module M looks \(M=M_ 1\oplus M_ 0\) such that f \(| M_ 1: M_ 1\to M_ 1\) is invertible and f \(| M_ 0: M_ 0\to M_ 0\) is nilpotent. Observing that this can be formulated in Jordan terms the author obtains a Fitting decomposition in Jordan algebras satisfying dcc on principal inner ideals. As an easy consequence the author obtains a new proof of the theorem that a unital J is local if no isotope of J contains a nontrivial idempotent. Similar results are obtained for Jordan pairs and Jordan triple systems.