JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.13, no.4, 2014 (SCI-Expanded)
Let F be a free Lie algebra of rank n >= 2 and R be a fully invariant ideal of F. We show that the test rank of the Lie algebra F/[R ', F] is equal to 1 when n is even and less than or equal to 2 when n is odd.