Abstract
In associative and alternative algebras a minimal ideal is either trivial or simple. This is not known for quadratic Jordan algebras. In the present note we show that a minimal ideal is either trivial or D \mathcal {D} -simple (possesses no proper ideals invariant under all inner derivations induced from the ambient algebra). In particular, the heart of any quadratic Jordan algebra is either trivial or D \mathcal {D} -simple. Hearts have recently played an important role in Zelmanov’s theory of prime Jordan algebras.
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