  Let $\Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring
$Q=\Bbbk[x_1,\ldots,x_n]$. In her thesis, Taylor introduced a complex which
provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda
constructed a differential graded structure on the Taylor resolution. More
recently, Avramov showed that this differential graded algebra admits divided
powers. We generalize each of these results to monomial ideals in a skew
polynomial ring $R$. Under the hypothesis that the skew commuting parameters
defining $R$ are roots of unity, we prove as an application that as $I$ varies
among all ideals generated by a fixed number of monomials of degree at least
two in $R$, there is only a finite number of possibilities for the Poincar\'{e}
series of $\Bbbk$ over $R/I$ and for the isomorphism classes of the homotopy
Lie algebra of $R/I$ in cohomological degree larger or equal to two.
