Subideals Of A Jordan Triple System

Presented in the first half of this work is a general discussion on the properties of subideals of an arbitrary triple systeni After giving a suitable concept of a subideal of a triple system, we show that both the image and the complete inverse image of a subideal under a epimorphism are again subideals. We then move on to the second half of the paper to investigate some further properties of subideals in a special kind of triple systemsordan triple systems. First of all, a subideal A of a Jordan triple system J is an ideal if A3=A. Secondly, any regular subideal of A is a regular ideal. Thirdly, if a strongly semiprime Jts. I has dc.c. on inner ideals, then a subideal of ~ is a strongly semiprime ideal of I. Finally, a subideal of a finite dimentional semisimple J.t.s. over a field ~ of characteristic 0 is an ideal.