Middle nucleus=center in semiprime Jordan algebras

Abstract

A. A. Albert showed that the middle nucleus and center coincide for a simple Jordan algebra finite-dimensional over a field of characteristic ≠ 2 \ne 2 . E. Kleinfeld extended this to arbitrary simple Jordan algebras of characteristic ≠ 2 \ne 2 . Recently this result has played a crucial role in the structure theory of E. Zelmanov. In this note we extend the result to linear Jordan algebras with no derivation-invariant trivial ideals.