Let k be a field and let I be a monomial ideal in the polynomial ring Q = k[x1, . . . , xn]. 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 k over R/I and for the isomorphism classes of the homotopy Lie algebra of R/I in cohomological degree larger or equal to two.
Ferraro, Luigi, Desiree Martin, and W. Frank Moore. 2023. “The Taylor Resolution over a Skew Polynomial Ring.” Journal of Algebra and Its Applications, August, 2550021. https://doi.org/10.1142/S0219498825500215
Journal of Algebra and Its Applications