  This work considers a natural generalization of primitivity with respect to a
language. Given a language $L$, a nonempty word $w$ is said to be $L$-primitive
if $w$ is not a proper power of any word in $L$. After ascertaining the number
of primitive words in submonoids of a free monoid, the work proceeds to count
$L$-primitive words in submonoids of a free monoid. The work also studies the
distribution of $L$-primitive words in certain subsets of free monoids.
