On annihilators in Jordan algebras (Q1802376)

After recalling the main features about annihilators of subsets of a Jordan algebra, the paper under review devotes a section to study annihilators in special Jordan algebras, relating them to the annihilators in the associative envelopes. Then, another section deals with annihilators in Jordan algebras with nonzero socle. Here it is also proved that any nondegenerate Jordan algebra satisfying the descending chain condition on the principal inner ideals, also satisfies the ascending chain condition on the annihilators of the principal inner ideals. Finally, annihilators in Jordan algebras without nilpotent elements and, in particular, in \(JB\)-algebras, are considered in the last section.