Strongly prime Jordan pairs with nonzero socle
The paper under review makes an interesting progress in the structure theory of Jordan systems. The notion of socle in Jordan systems has become an interesting tool in the development of this Jordan structure theory. The definition of socle for Jordan algebras is due to Osborn and Racine while for Jordan triples and Jordan pairs it was extended by Fernández-Lopez, García-Rus, Sánchez-Campos and Loos, respectively. In previous papers, the authors obtained, under some restrictions on the characteristic, structure theorems for strongly prime Jordan systems (algebras, triples and pairs) with nonzero socle. Jordan algebras and Jordan pairs of infinite capacity were also determined by the authors without any restriction in another paper. In the paper under review they obtain a characteristic-free description of strongly prime Jordan pairs with minimal inner ideals.
scientific article; zbMATH DE number 1965508