Global ETD Search

21	Complexidade de Módulos / Complexity of Modules Silvana Kameyama 16 February 2012 (has links) A complexidade de um módulo M, sobre uma álgebra de dimensão finita R, é a medida do crescimento da dimensão de suas sizigias. No nosso trabalho, estudamos esse conceito, nos concentrando muito mais no caso das álgebras autoinjetiva. Relacionamos esse crescimento com o comportamento da componente do carcás de Auslander-Reiten, a qual o módulo M pertence. Em particular, estudamos, com bastante cuidado, o caso em que a complexidade é 1, o que significa que a dimensão das sizigias são eventualmente constante. Surpreendentemente, o comportamento de todos os módulos numa mesma componente é muito parecido. / The complexity of a module M under a finite dimensional algebra R is the measure of the growth of its syzygies\' dimension. In our work, we study this concept concentrating on the case of the selfinjective algebras. We relate this growth with the behavior of the Auslander-Reiten component containing this module. In particular, we study, carefully, the case in which the complexity is 1. Surprisingly, the behavior of every module in the same component as M is very similar. álgebras autoinjetivas Álgebras de Artin carcás de Auslander-Reiten complexidade números Betti resoluções projetivas sequências de Auslander-Reiten. Artin algebras Auslander-Reiten quiver Auslander-Reiten sequences. Betti numbers complexity projectives resolutions selfinjective algebras
22	On Partial Regularities and Monomial Preorders Nguyen, Thi Van Anh 28 June 2018 (has links) My 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. 31.23 - Ideale, Ringe, Moduln, Algebren 13-02 - Research exposition ddc:510
23	l<sup>p</sup>-Kohomologie, insbesondere Verschwindungssätze für l<sup>p</sup>-Kohomologie / l<sup>p</sup>-cohomology, in particular vanishing theorems for l<sup>p</sup>-cohomology Kappos, Elias 10 July 2007 (has links) No description available. 510 Mathematik Mathematics and Computer Science lp-Kohomologie diskrete Gruppen Gruppen vom Typ FPn lp-Bettizahlen lp-cohomology diskrete groups groups of type FPn lp-Betti numbers 31.61 31.21
24	Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture / Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture Knebusch, Anselm 19 October 2009 (has links) No description available. 510 Mathematik EEGL 000 Selfadjoint operator algebras EEGM 200 Methods of algebraic topology Mathematics and Natural Science Betti-Zahlen von Neumann-Algebren Operatortheorie G-CW-Komplex Approximation Atiyah Vermutung Betti-numbers von Neumann-algebras operatortheory G-CW-complex approximation Atiyah conjecture 31.55 Globale Analysis 31.47 Operatortheorie

Page generated in 0.0534 seconds