On the Exterior Degree of a Finite-Dimensional Lie Algebra

In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi mathvariant="double-struck">F</a:mi></a:mrow><a:mrow><a:mi>q</a:mi></a:mrow></a:msub></a:math> and give upper and lower bounds. Also, we give some relations between this concept and commutativity degree, capability, and Schur multiplier.