Affine Monoids, Hilbert Bases and Hilbert Functions

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003071115
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dc.contributor.advisorProf. Dr. Winfried Bruns
dc.creatorKoch, Robert
dc.date.accessioned2010-01-30T14:50:30Z
dc.date.available2010-01-30T14:50:30Z
dc.date.issued2003-07-11T12:04:51Z
dc.date.submitted2003-07-11T12:04:51Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003071115-
dc.description.abstractThe aim of this thesis is to introduce the reader to the theory of affine monoids and, thereby, to present some results. We therefore start with some auxiliary sections, containing general introductions to convex geometry, affine monoids and their algebras, Hilbert functions and Hilbert series. One central part of the thesis then is the description of an algorithm for computing the integral closure of an affine monoid. The algorithm has been implemented, in the computer program `normaliz´; it outputs the Hilbert basis and the Hilbert function of the integral closure (if the monoid is positive). Possible applications include: finding the lattice points in a lattice polytope, computing the integral closure of a monomial ideal and solving Diophantine systems of linear inequalities. The other main part takes up the notion of multigraded Hilbert function: we investigate the effect of the growth of the Hilbert function along arithmetic progressions (within the grading set) on global growth. This study is motivated by the case of a finitely generated module over a homogeneous ring: there, the Hilbert function grows with a degree which is well determined by the degree of the Hilbert polynomial (and the Krull dimension).eng
dc.language.isoeng
dc.subjectaffine monoid
dc.subjectintegral closure
dc.subjectnormalization
dc.subjectHilbert basis
dc.subjectHilbert function
dc.subjectaffine monoid algebra
dc.subjectsemigroup ring
dc.subject.ddc510 - Mathematikger
dc.titleAffine Monoids, Hilbert Bases and Hilbert Functionseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2003-05-26T12:00:00Z-
elib.elibid223-
elib.marc.edtfangmeier-
elib.dct.accessRightsa-
elib.dct.created2003-06-06T11:47:27Z-
elib.dct.modified2003-07-11T12:04:51Z-
dc.contributor.refereeProf. Dr. Udo Vetter
dc.subject.msc13B22eng
dc.subject.msc13D40eng
dc.subject.msc13P99eng
dc.subject.msc20M25eng
dc.subject.msc52B20eng
dc.subject.dnb27 - Mathematikger
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