Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Nov. 25, 2008). PDF text: v, 87 p. : ill. ; 792 K. UMI publication number: AAT 3315051. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph.D) -- University of Texas at Arlington, 2009.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 20, 2009) Vita. Includes bibliographical references.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed Oct. 10, 2007). PDF text: 127 p. : ill. UMI publication number: AAT 3258773. Includes bibliographical references. Also available in microfilm and microfiche formats.

This thesis consists of two parts. Part one revolves around a construction for homogeneous Gorenstein ideals and properties of these ideals. Part two focuses on the behavior of the Boij-Söderberg decomposition of lex ideals. Gorenstein ideals are known for their nice duality properties. For codimension two and three, the structures of Gorenstein ideals have been established by Hilbert-Burch and Buchsbaum-Eisenbud, respectively. However, although some important results have been found about Gorenstein ideals of higher codimension, there is no structure theorem proven for higher codimension cases. Kustin and Miller showed how to construct a Gorenstein ideals in local Gorenstein rings starting from smaller such ideals. A modification of their construction in the case of graded rings is discussed. In a Noetherian ring, for a given two homogeneous Gorenstein ideals, we construct another homogeneous Gorenstein ideal and so we describe the resulting ideal in terms of the initial homogeneous Gorenstein ideals. Gorenstein liaison theory plays a central role in this construction. Using liaison properties, we examine structural relations between the constructed homogeneous ideal and the starting ideals. Boij-Söderberg theory is a very recent theory. It arose from two conjectures given by Boij and Söderberg and their proof by Eisenbud and Schreyer. It establishes a unique decomposition for Betti diagram of graded modules over polynomial rings. In the second part of this thesis, we focus on Betti diagrams of lex ideals which are the ideals having the largest Betti numbers among the ideals with the same Hilbert function. We describe Boij-Söderberg decomposition of a lex ideal in terms of Boij-Söderberg decompositions of some related lex ideals.

We study the Cohen-Macaulay property of Rees algebras of modules of Kähler differentials. When the module of differentials has projective dimension one, it is known that condition $F_1$ is sufficient for the Rees algebra to be Cohen-Macaulay. The converse was proved if the module of differentials is already $F_0$. We weaken the condition $F_0$ globally by assuming some homogeneity condition.<br> <br> We are also interested in the defining ideal of the Rees algebra of a Jacobian module. If the Jacobian module is an ideal, we prove a formula for computing the defining ideal. Using the formula, we give an explicit description of the defining ideal in the monomial case. From there, we characterize the Cohen-Macaulay property of the Rees algebra.<br> <br> In the last chapter, we study Gorenstein linkage mostly in the graded case. In particular, we give an explicit example of a class of monomial ideals that are in the homogeneous Gorenstein linkage class of a complete intersection. To do so, we prove a Gorenstein double linkage construction that is analogous to Gorenstein biliaison.

Seja (R;m) um anel Noetheriano local e R \'CONTÉM\' \'iota IND. 1\' \'CONTÉM\' \'iota IND. 2\' \'CONTÉM ... uma filtração de ideais de R. Podemos então construir a álgebra graduada F(\'\\Im) := \'SOMA DIRETA IND. n > OU = 0 POT. \'iota IND. n / \'m \'iota IND. n\', chamada de fibra especial. Esta tese objetiva a pesquisa deste anel. Investigamos sobre a sua propriedade de ser Gorenstein e a sua regularidade de Castelnuovo-Mumford. Outro objetivo, é generalizarmos o teorema de Risler-Teissier (sobre multiplicidades mistas) para o caso de filtrações de Hilbert / Let (R;m) be a Noetherian local ring and R \'CONTAINS\' \'iota IND. 1\' \'CONTAINS\' \'iota IND. 2\' \'CONTAINS\' ... a filtration of ideals in R. We may then construct the graded algebra F(\\Im) := \'DIRECT SUM\' IND. n > OR = \'0 POT. \'iota\' IND. n / \'m \'iota IND. n\' , which is called fiber cone. This thesis has the goal to research about this graded ring. We investigate its Gorenstein property and its Castelnuovo-Mumford regularity. Another aim is to generalize the Risler-Teissiers theorem (about mixed multiplicities) for the case of Hilbert filtration

Seja (R;m) um anel Noetheriano local e R \'CONTÉM\' \'iota IND. 1\' \'CONTÉM\' \'iota IND. 2\' \'CONTÉM ... uma filtração de ideais de R. Podemos então construir a álgebra graduada F(\'\\Im) := \'SOMA DIRETA IND. n > OU = 0 POT. \'iota IND. n / \'m \'iota IND. n\', chamada de fibra especial. Esta tese objetiva a pesquisa deste anel. Investigamos sobre a sua propriedade de ser Gorenstein e a sua regularidade de Castelnuovo-Mumford. Outro objetivo, é generalizarmos o teorema de Risler-Teissier (sobre multiplicidades mistas) para o caso de filtrações de Hilbert / Let (R;m) be a Noetherian local ring and R \'CONTAINS\' \'iota IND. 1\' \'CONTAINS\' \'iota IND. 2\' \'CONTAINS\' ... a filtration of ideals in R. We may then construct the graded algebra F(\\Im) := \'DIRECT SUM\' IND. n > OR = \'0 POT. \'iota\' IND. n / \'m \'iota IND. n\' , which is called fiber cone. This thesis has the goal to research about this graded ring. We investigate its Gorenstein property and its Castelnuovo-Mumford regularity. Another aim is to generalize the Risler-Teissiers theorem (about mixed multiplicities) for the case of Hilbert filtration

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-16T11:59:48Z No. of bitstreams: 1 arquivototal.pdf: 1814472 bytes, checksum: 50307319d745b002230f3dadb2039246 (MD5) / Made available in DSpace on 2017-08-16T11:59:48Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1814472 bytes, checksum: 50307319d745b002230f3dadb2039246 (MD5) Previous issue date: 2016-08-09 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this dissertation, we study the so-called totally re°exive modules and the notion of Goren-stein dimension over Noetherian commutative rings. The main purpose is to prove the important Auslander-Bridger formula and the Gorenstein theorem, which will allow us to characterize Goren-stein local rings through total re°exivity, as well as to provide su±cient conditions for the property of G-regularity. We furnish, moreover, interesting examples and counterexamples. / Nesta disserta»c~ao, estudamos os chamados m¶odulos totalmente re°exivos e a no»c~ao de dimens~ao de Gorenstein sobre an¶eis comutativos Noetherianos. A principal ¯nalidade ¶e demonstrar a impor- tante f¶ormula de Auslander-Bridger e o Teorema de Gorenstein, o que permitir¶a caracterizar an¶eis locais Gorenstein atrav¶es de re°exividade total, bem como apresentar condi»c~oes su¯cientes para a propriedade de G-regularidade. Fornecemos, tamb¶em, exemplos e contra-exemplos interessantes.

This paper is an overview of the developments and generalizations of Tate Cohomology. The number of such generalizations is high and the literature on many of them is vast. Hence, we do not pretend to give a complete account of all the branches that have developed from the original ideas of Tate. This is rather an overview of how the ideas developed. / Este artículo es una revisión del desarrollo y generalizaciones de la cohomología de Tate. El número de tales generalizaciones es alto y la literatura en torno a muchas de ellas es vasta. Por consiguiente, no pretendemos dar un recuento completo de las ramas que se desprenden de las ideas originales de Tate; esto más bien representa un bosquejo de cómo estas ideas se han ido desarrollando.