FIELDS AND RINGS AND ALGEBRAS

Author: ARANDA PINO GONZALO.
Year: 2004.
University: MÁLAGA [www.uma.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAAD DE CIENCIAS.

Summary: Most of the thesis can be seen as a development of the theory of systems ratios of certain types of algebraic objects associative and not necasariamente conmutativos or element unidad.Así, the first objective is to build systems ratios in a number of contexts where the absence of them, and it was clear (in addition to the clear interest to rely on notions of appropriate structures ratios in new situations is by itself) as a result, be able to achieve further progress in the knowledge of certain systems using this theory ratios. As new construction achieved a satisfactory algebra of quotients porla left graduate maximal torque along with notions of associative ratios from the left maximal (in a broader situation that previously considered by M. Gomez Lozano Siles and M. Molina) and triple system ratios on the left maximal. Among the applications systems ratios from the left maximal show some results on Morita-invariabilidad (through rings corner) and a theorem Johnson for a certain type of algebra class graduates by Z. The last chapter of this thesis is devoted to algebra Highway Leavitt on grafos.Estas algebras include some of those who had been appearing on our presentations previas.En notably include algebra to polynomials Laurent K (x, y-1), they are (in our view) the simplest example where different concepts of algebra of quotients from the left and graduated maximal algebra of quotients from the left maximal (without rank). our task to find theoretical terms on a graph, necessary and enough so that the algebra of roads Leavitt. Taken as a ring, have a certain propiedad.Concretamente, we do this for simpmlicidad and the purely infinite.

Author: SACRISTÁN TOBÍAS SARA.
Year: 2004.
University: LA RIOJA [www.unirioja.es].
Place of defense: UNIVERSIDAD DE LA RIOJA.
Place of preparation: UNIVERSIDAD DE LA RIOJA.

Summary: In line with previous works of E. Dynkin (in 1952) for groups and Lie algebras, and M. Racine (1974) and A. Elduque (in 1984) for simple associative algebra, alternatives, Jordan and Malcev in this Report thesis explores the subálgebras maximal certain algebraic structures to which they were called in Physics and is still calling superálgebras (emerged with the theory unification physics known as Supersimetría). A superálgebra is an algebra Z2 graded. The ultimate goal is to put classify subálgebras maximales de superálgbras Jordan simple finite dimensional. A superálgebra Jordan algebra is not a graduate of Jordan on Z2. It can be defined in terms of graduates or identities saying it is a superálgebra such that their envelope is a Grassmann algebra Jordan. As several of the types of superálgebras Jordan simple finite dimensional from superálgebra Organizations (yes these are algebras associative Z2 graduates without more), you need to first sort the subálgebras maximales de superálgebras simple finite dimensional and superálgebras associative with simple finite dimensional superinvolución. This is accomplished entirely not the case in Jordan, where some situations are open. In the course of this work are obtained other results as regards the study group automorphisms of superálgebra Jordan simple call Kac.

Author: GARCIA ROMAN MARIA DEL SOCORRO.
Year: 2005.
University: LA LAGUNA [www.ull.es].
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS UNIVERSISDAD DE LA LAGUNA.

Author: ORTEGA ESPARZA EDUARD.
Year: 2005.
University: AUTÓNOMA DE BARCELONA [www.uab.es].
Place of defense: DEPARTAMENTO DE MATEMÁTICAS.
Place of preparation: UNIVERSIDAD AUTÓNOMA DE BARCELONA.

Author: Cortés Izurdiaga Manuel.
Year: 2005.
University: ALMERÍA [www.ual.es].
Place of defense: F.Ciencias Experimentales.
Place of preparation: Facultad Ciencias Experimentales.

Author: Brustenga Bort Miquel.
Year: 2006.
University: AUTÓNOMA DE BARCELONA [www.uab.es].
Place of defense: Facultat de Ciències.
Place of preparation: Facultat de Ciències.

Summary: In this dissertation explores various algebras associated with a quiver (directed graph). Mainly, the algebra of roads, algebra and the algebra of Leavitt regulate a quiver. Remarkably, for all quiver columna-finito get a ring regularly (in the sense of von Neumann), which we are able to calculate its monoide class isomorfía modules proyectivos finitamente generated. This result represents an important contribution to the Problem of Conduct for Rings Regular von Neumann. Moreover, we study the category of modules finitamente submitted on the algebra of Leavitt and the group of Whitehead of the various rings studied.