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1	Module theory over the exterior algebra with applications to combinatorics Kämpf, Gesa 17 May 2010 (has links) Diese Arbeit entwickelt aufbauend auf bekannten Resultaten die Modultheorie über der äußeren Algebra in Teilen weiter, insbesondere werden die Tiefe eines Moduls und Moduln mit linearer injektiver Auflösung untersucht. Angewendet werden die Resultate auf die Orlik-Solomon Algebra eines Matroids. Exterior algebra Orlik-Solomon algebra face ring Matroid 31.23 - Ideale, Ringe, Moduln, Algebren 31.12 - Kombinatorik, Graphentheorie ddc:510
2	The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement Le, Van Dinh 17 February 2016 (has links) My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic polynomial of a matroid are encoded in the f-vector of the broken circuit complex of the matroid. Among main results of the thesis are characterizations of the complete intersection and Gorenstein properties of the broken circuit complex and the Orlik-Terao algebra. I also study the h-vector of the broken circuit complex of a series-parallel network and relate certain entries of that vector to ear decompositions of the network. An application of the Orlik-Terao algebra in studying the relation space of a hyperplane arrangement is also included in the thesis. Broken circuit complex Hyperplane arrangement Orlik - Terao algebra h-vector Relation space Complete intersection Gorenstein Linear resolution Series - parallel network Matroid 31.12 - Kombinatorik, Graphentheorie 31.23 - Ideale, Ringe, Moduln, Algebren ddc:510
3	Content Algebras and Zero-Divisors / Inhaltsalgebren und Nullteiler Nasehpour, Peyman 10 February 2011 (has links) This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{~is an ideal of~} R \text{~and~} x \in IM \rbrace $. $M$ is said to be a \textit{content} $R$-module if $x \in c(x)M $, for all $x \in M$. The $R$-algebra $B$ is called a \textit{content} $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In chapter 2, it is proved that in content extensions, minimal primes extend to minimal primes, and zero-divisors of a content algebra over a ring which has Property (A) or whose set of zero-divisors is a finite union of prime ideals are discussed. The preservation of diameter of zero-divisor graph under content extensions is also examined. Gaussian and Armendariz algebras and localization of content algebras at the multiplicatively closed set $S^ \prime = \lbrace f \in B \colon c(f) = R \rbrace$ are considered as well. In chapter 3, the second topic of the thesis, that is about the grade of the zero-divisor modules, is discussed. Let $R$ be a commutative ring, $I$ a finitely generated ideal of $R$, and $M$ a zero-divisor $R$-module. It is shown that the $M$-grade of $I$ defined by the Koszul complex is consistent with the definition of $M$-grade of $I$ defined by the length of maximal $M$-sequences in I$. Chapter 1 is a preliminarily chapter and dedicated to the introduction of content modules and also locally Nakayama modules. content module content algebra locally Nakayama module weak content algebra few zero-divisors Gaussian algebra Armendariz algebra zero-divisor graph Grade homological dimension Property (A) Zero-divisor module semigroup ring semigroup module local cohomological module McCoy's property minimal prime primal ring 31.23 - Ideale, Ringe, Moduln, Algebren 31.12 - Kombinatorik, Graphentheorie 13-02 - Research exposition ddc:510
4	Delay Management in Public Transportation: Capacities, Robustness, and Integration / Anschlusssicherung im Öffentlichen Verkehr: Kapazitäten, Robustheit und Integration Schachtebeck, Michael 17 December 2009 (has links) No description available. 510 Mathematik Mathematics and Computer Science Anschlusssicherung Kapazitätsrestriktionen ganzzahlige Programmierung Reduktionsverfahren Heuristiken delay management capacity constraints integer programming reduction techniques heuristics 31.12 31.80 85.03 EJAB 060: Transportation logistics {Operations research LCC 024: Operations Research Optimierung {Wirtschaftsmathematik}

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