  We generalize Baranov and Shlaka's results about bar-minimal Jordan-Lie and
regular inner ideals of finite dimensional associative algebras. Let A be a
finite dimensional 1-perfect associative algebras A over an algebraically
closed field \mathbb{F} of characteristic p\ge0 and let A' be a subalgebra of
A. We prove that for any bar-minimal Jordan-Lie inner ideal B' a A', there is a
bar-minimal Jordan-Lie inner ideal of A that contains B' and if B' is regular,
then is a regular inner ideal of A that contains B'. We also prove that for any
strict orthogonal pair (e',f') in A', there is a strict orthogonal idempotent
pair (e,f) in A such that e'A'f'\subseteq eAf
