Ideally constrained Lie algebras

In this paper we deal with graded Lie algebras L such that there exists a positive integer r such that for every positive integer i and for every homogeneous ideal I ⊈ Li the inclusion I ⊇ Li+r-1 holds. The solvable case and the r = 1 case receive a special attention. © 2002 Elsevier Science (USA). All rights reserved.