# Minimal generating sets of free algebras of varieties

Let $V$ be a variety and $F$ be a relatively free algebra in $V$. Suppose $X$ is a minimal generating set for $F$. Under what conditions we can deduce that $X$ is a free basis of $F$?

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Is X finite? Then V generated by finite algebras works. –  Benjamin Steinberg Mar 24 '14 at 16:15
Yes $X$ is finite. –  M. Shahryari Mar 24 '14 at 16:26