School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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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.


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Journal of Algebra and Its Applications



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Mathematics Commons



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