Take $S$ and $T$ two subsets of homogeneous elements of the associative noncommutative free algebra $F$ over a field $k$ generated by a set $X$, provided with a positive grading. To exclude pathologies $S$ and $T$ are contained in $F.F$. If $S$ and $T$ are minimal generator sets for their respective generated ideals, is it the same true for the set $S.T$ of products of elements of $S$ and $T$?