A note on the tensor product of Lie soluble algebras

摘要

D. M. Riley proved in [3] that, if A and B are either Lie nilpotent or Lie metabelian algebras, then their tensor product A circle times B is Lie soluble and obtained bounds on the Lie derived length of A circle times B. The aim of the present note is to improve Riley's bounds; moreover we consider also the cases in which A and B are either strongly Lie soluble or strongly Lie nilpotent algebras.