Theses and Dissertations

Date of Award

5-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Luigi Ferraro

Second Advisor

Timothy Huber

Third Advisor

Debanjana Kundu

Abstract

Let k be a field, and let I be a monomial ideal in the polynomial ring R = k[x1,..., xn]. In her thesis, Taylor introduced a complex that yields a finite free resolution of R/I as an R-module. Building on Taylor’s work, Ferraro, Martin, and Moore extended this construction to monomial ideals in skew polynomial rings. Because the Taylor resolution is typically not minimal, subsequent research efforts went into identifying specific classes of ideals whose minimal free resolutions can be constructed more simply. In 1990, Eliahou and Kervaire devised an approach for handling minimal resolutions of certain monomial ideals R, namely stable ideals. This work was later generalized to skew polynomial rings by Ferraro and Hardesty. Furthermore in 2002, Herzog and Takayama provided a minimal free resolution for monomial ideals with linear quotients, a broader class encompassing stable ideals; in the stable case, their resolution reduces to the Eliahou–Kervaire resolution. In this thesis, we extend the Herzog–Takayama resolution to the setting of skew polynomial rings.

Comments

Copyright 2025 Linoy Utkina. https://proquest.com/docview/3240626342

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