Local-to-global inheritance of primitivity in Jordan algebras
The authors show the inheritance of primitivity by a strongly prime Jordan algebra from any of its primitive local algebras. Unlike the algebra case, primitivity of a Jordan pair is considered at a particular element, and shown to be equivalent to primitivity of its local algebra at this element under the assumption of strong primeness. In this context, the above result has played an important role in the definite solution of the problem on the ``location'' of primitivity for Jordan systems [\textit{J. A. Anquela} and \textit{T. Cortés}, J. Algebra 202, 295-314 (1998)], that is, the possibility of changing the element at which primitivity occurs.
scientific article; zbMATH DE number 1145759