Mathematics
Permanent URI for this collectionhttps://hdl.handle.net/11274/15373
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Browsing Mathematics by Author "Hardesty, Alexis"
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Item The Eliahou-Kervaire resolution over a skew polynomial ring(Taylor & Francis, 2023) Ferraro, Luigi; Hardesty, AlexisIn a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a class of monomial ideals in a polynomial ring, called stable ideals. As a consequence of their construction they deduced several homological properties of stable ideals. Furthermore they showed that this resolution admits an associative, graded commutative product that satisfies the Leibniz rule. In this paper we show that their construction can be extended to stable ideals in skew polynomial rings. As a consequence we show that the homological properties of stable ideals proved by Eliahou and Kervaire hold also for stable ideals in skew polynomial rings.Item The Tor algebra of trimmings of Gorenstein ideals(Springer, 2023) Ferraro, Luigi; Hardesty, AlexisLet (R,m,k) be a regular local ring of dimension 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by m; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R=J and compute a partial DG algebra structure on this resolution. We provide the full DG algebra structure in the appendix. We use the products on this resolution to study the Tor algebra of such trimmed ideals and we use the information obtained to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class G hold true in our context. Furthermore, we address the realizability question for ideals of class G.