In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating the first Pontrjagin class for an arbitrary quaternionic toric 8-manifold.

Trata sobre la teoría de haces y esquemas. El objetivo principal es desarrollar detalladamente un teorema de J.-P. Serre (en el libro de Hartshorne [6], aparece como ejercicio (5.9) del capítulo II) que establece la correspondencia entre haces coherentes sobre esquemas proyectivos y módulos graduados de tipo casi infinito. Además, usando métodos cohomológicos, da una generalización de este teorema de Serre. Asimismo se redacta la solución de otros ejercicios de [6] que son necesarios para la solución del ejercicio principal, los cuales son presentadas por medio de proposiciones y teoremas. / Tesis

This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. In the final section of the main text solvable extensions are studied and the Abel-Ruffini theorem is proved. The discussion section gives a brief overview of analytic methods of solving polynomial-equations. / Den här uppsatsen utforskar Galoisteorin för att bevisa Abel-Ruffinis sats. I den första delen är algebraiska strukturer i fokus: Grupper, ringar, kroppar, etc. Efter detta intrduceras polynom-ringar, och fokuset vänds sedan till ändliga kropps-utvidgningar. I den sista delen av huvudtexten så studeras lösbara förvidgningar och Abel-Ruffini's sats bevisas. Diskusionen ger en översikt över analytiska lösningar av polynom-ekvationer.

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<p>This study examines what growing old means for the older women's sense of self-identity. Some gerontologists argue that old age constitutes a period of role loss with detrimental impact on identity. A sizable body of data do not support this assumption. The underlying assumption of this study is that identity emerges and is sustained through social interaction. Thus the research focuses on (1) the meaning of 'being old' as defined by older women and (2) the extent to which a positive identity can be retained through social network involvement with family, friends and community leisure activities. Instead of focusing on what is lost, the emphasis was on determining what role relationships are retained and established in old age, and the extent to which these serve to maintain a positive self image.</p> <p>The research is based on interviews with 142 women over age 65 living in the town of Bridgewater, Nova Scotia. The principle component of this sample comprised 101 women living in their own homes or apartments (i.e. community- dwelling). Most of the analysis is based on this sample. However, where comparative analysis is useful, these data are supplemented with information from interviews with 31 residents of senior citizen apartment complexes and 10 residents of a nursing home. The findings indicate that the elderly women studied here generally do not view themselves as 'elderly' or 'old'. Age identity is found to be largely situational and more relevant to some interactions than others. The majority have managed to retain a positive identity which is deeply embedded within their informal role involvements and social network ties. As a result, the loss of more formal role relationships had only limited impact on identity. The findings also indicate that a relatively stable small community appears to offer advantages for identity management in old age.</p> / Doctor of Philosophy (PhD)

In this paper, for a select group of quadratic algebras, we investigate restrictions necessary on the generators of the ideal for the resulting algebra to be Koszul. Techniques include the use of Gröbner bases and development of Koszul resolutions. When the quadratic algebra is Koszul, we provide the associated linear resolution of the field. When not Koszul, we describe the maps of the resolution up to the instance of nonlinearity. / Ph. D.