On the socle of a Jordan pair
The author studies the socle Soc V\(=(Soc V^+,Soc V^-)\) of a Jordan pair \(V=(V^+,V^-)\) where Soc \(V^{\sigma}\) is the sum of all inner ideals of \(V^{\sigma}\) that are simple or trivial. For nondegenerate V he characterizes the elements of Soc \(V^+\) by showing \(u\in Soc V^+\) if and only if the inner ideal generated by u has dcc on principal inner ideals. The socle is shown to be a direct sum of simple ideals. Moreover, the socle allows a description as direct limit of subpairs of finite capacity.
scientific article; zbMATH DE number 4204626