  The motivation for this paper has been to study the relation between the zero
component of the maximal graded algebra of quotients and the maximal graded
algebra of quotients of the zero component, both in the Lie case and when
considering Martindale algebras of quotients in the associative setting. We
apply our results to prove that the finitary complex Lie algebras are (graded)
strongly nondegenerate and compute their maximal algebras of quotients.
