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dc.contributor.authorPainter, Jared Lafayetteen_US
dc.date.accessioned2012-07-25T19:08:44Z
dc.date.available2012-07-25T19:08:44Z
dc.date.issued2012-07-25
dc.date.submittedJanuary 2012en_US
dc.identifier.otherDISS-11702en_US
dc.identifier.urihttp://hdl.handle.net/10106/11056
dc.description.abstractIn this manuscript we explore properties of minimal free resolutions and their relationship to the Tor-algebra structure for trivariate monomial ideals. We begin with an in-depth analysis of minimal free resolutions of S = R / I, where R = k[x; y; z] is a polynomial ring over a field k, and I is a monomial ideal that is primary to the homogeneous maximal ideal m of R. We will de ne a special form of the minimal free resolution of S, and then determine when we get nonzero elements from I as entries in the matrices of the resolution. We find a complete answer to this question for the second matrix of our special resolution for all trivariate monomial ideals. For the third matrix, we provide a complete answer for generic monomial ideals. We also observe differences for resolutions of generic monomial ideals in comparison to non-generic monomial ideals. We will find that our results on free resolutions relate to the Tor-algebra structure for S. In [4] Avramov describes the Tor-algebra structure A = TorR(k; S), for rings of codepth 3. His description of this structure is comprised of 5 categories. We will explore this structure, and will determine which of the 5 categories can be realized by monomial ideals. We will also learn how to describe the Tor-algebra structure from the minimal free resolution of S. Finally, we will find classes of monomial ideals with the desired Tor-algebra structure, and give a complete classification for generic monomial ideals.en_US
dc.description.sponsorshipJorgensen, David A.en_US
dc.language.isoenen_US
dc.publisherMathematicsen_US
dc.titleResolutions And Tor Algebra Structures For Trivariate Monomial Idealsen_US
dc.typePh.D.en_US
dc.contributor.committeeChairJorgensen, David A.en_US
dc.degree.departmentMathematicsen_US
dc.degree.disciplineMathematicsen_US
dc.degree.grantorUniversity of Texas at Arlingtonen_US
dc.degree.leveldoctoralen_US
dc.degree.namePh.D.en_US


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