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On Partial Regularities and Monomial Preorders

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823
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dc.contributor.advisorProf. Dr. Tim Römerger
dc.creatorNguyen, Thi Van Anh-
dc.date.accessioned2018-06-28T12:13:04Z-
dc.date.available2018-06-28T12:13:04Z-
dc.date.issued2018-06-28T12:13:05Z-
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823-
dc.description.abstractMy PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.eng
dc.rightsNamensnennung-NichtKommerziell-KeineBearbeitung 3.0 Deutschland-
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/de/-
dc.subjectpartial regularities, monomial preorders, Castelnuovo-Mumford regularity, filter-regular sequences, Local Duality Theorem, a-invariants, b-invariants, Betti-numbers, leading term ideals, flat deformations, weight orderseng
dc.subject.ddc510 - Mathematikger
dc.titleOn Partial Regularities and Monomial Preorderseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2018-06-22-
dc.contributor.refereeProf. Dr. Ngo Viet Trungger
dc.subject.bk31.23 - Ideale, Ringe, Moduln, Algebrenger
dc.subject.msc13-02 - Research expositionger
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