Nilideals of Jordan triple systems with finiteness conditions (Q1065140)

The main results of this paper are as follows: 1) A quasi-regular ideal I of a Jordan triple system (Jordan pair) J which satisfies the minimal condition for inner ideals of J contained in I is nilpotent, and I is also an Artinian module over the ring of scalars. 2) A nil ideal I of a Jordan triple system (Jordan pair) J which satisfies the maximal condition for inner ideals of J contained in I is nilpotent, and I is also a Noetherian module over the ring of scalars. 3) If N is a nil subalgebra of a Jordan algebra which satisfies a chain condition on annihilators, then N is solvable.