Local inheritance in Jordan algebras
The authors prove that local algebras of a Jordan algebra inherit nondegeneracy, strong primeness, primitivity and semi-primitivity. Two main cases are to consider: algebras with a nonzero hermitian part, and PI algebras. Non PI strong prime Jordan algebras are first considered, then non PI primitive Jordan algebras, and finally PI primitive Jordan algebras. The main result is: Let \(J\) be a Jordan algebra, \(0\neq a\in J\). If \(J\) is nondegenerate, \(J_ a\) is nondegenerate. If \(J\) is primitive, \(J_ a\) is primitive. If \(J\) is strongly prime, \(J_ a\) is strongly prime. If \(J\) is semiprimitive, \(J_ a\) is semiprimitive.
scientific article; zbMATH DE number 769518