We will discuss some properties of Jordan and Lie homomorphisms and derivations on prime rings. We first give some definitions and then we show some classic results .

O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert. / The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.

O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert. / The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.

We generalize the results of Leger and Luks and other researchers about generalized derivations to the cases of ternary Lie algebras and n-BiHom Lie algebras. We investigate the derivations algebras of ternary Lie algebras induced from Lie algebras, we explore the subalgebra of quasi-derivations and give their properties. Moreover, we give a classification of the derivations algebras for low dimensional ternary Lie algebras. For the class of n-BiHom Lie algebras, we study the algebras of generalized derivations and prove that the algebra of quasi-derivations can be embedded in the derivation algebra of a larger n-BiHom Lie algebra.

This dissertation explores aspects of the representation theory for tensor algebras, which are non-selfadjoint operator algebras Muhly and Solel introduced in 1998, by developing a cohomology theory for completely bounded Hilbert modules. Similar theories have been developed for Banach modules by Johnson in 1970, for operator modules by Paulsen in 1997, and for Hilbert modules over the disc algebra by Carlson and Clark in 1995. The framework presented here was motivated by a desire to further understand the completely bounded representation theory for tensor algebras on Hilbert spaces. The focal point of this thesis is the first Ext group, Ext1, which is defined as equivalence classes of short exact sequences of completely bounded Hilbert modules. Alternate descriptions of this group are presented. For general operator algebras, Ext1 can be realized as the collection completely bounded derivations equivalent up to an inner derivation. When the operator algebra is a tensor algebra, Ext1 can be described as a quotient space of intertwining operators, a description analogous to a result of Ferguson in 1996 in the case of the classical disc algebra. A theorem of Sz.-Nagy and Foias from 1967, concerning contractions in triangular form, is applied to analyze derivations that are off-diagonal corners of completely contractive representations. It is proved that, in some cases, this analysis determines when all derivations must be inner or suggests ways to construct non-inner derivations. In the third chapter, a characterization is given of completely bounded representations of a tensor algebra in terms of similarities of contractive intertwiners. Also proven is that for a Csup*;-correspondence X over a Csup*;-algebra A and the Toeplitz algebra T(X), Mn(T(X))= T(Mn(X)). The analogous statement for tensor algebras is deduced as a corollary. In the final chapter, a brief survey of non-abelian category theory is provided. Extensions of completely bounded Hilbert modules over operator algebras are defined. Theorems asserting the projectivity of isometric modules and injectivity of coisometric modules by Carlson, Clark, Foias, and Williams in 1995 are generalized to the noncommutative setting of tensor algebras using commutant lifting. A result of Popesecu in 1996 for noncommutative disc algebras is also covered in the general framework of this thesis.

Thesis (M. Sc.)--Carleton University, 2000. / Includes bibliographical references. Also available in electronic format on the Internet.

Parsability approaches of several grammar formalisms generating also non-context-free languages are explored. Chomsky grammars, Lindenmayer systems, grammars with controlled derivations, and grammar systems are treated. Formal properties of these mechanisms are investigated, when they are used as language acceptors. Furthermore, cooperating distributed grammar systems are restricted so that efficient deterministic parsing without backtracking becomes possible. For this class of grammar systems, the parsing algorithm is presented and the feature of leftmost derivations is investigated in detail. / Ansätze zum Parsing verschiedener Grammatikformalismen, die auch nicht-kontextfreie Sprachen erzeugen können, werden diskutiert. Chomsky-Grammatiken, Lindenmayer-Systeme, Grammatiken mit gesteuerten Ersetzungen und Grammatiksysteme werden behandelt. Formale Eigenschaften dieser Mechanismen als Akzeptoren von Sprachen werden untersucht. Weiterhin werden kooperierende verteilte (CD) Grammatiksysteme derart beschränkt, dass effizientes deterministisches Parsing ohne Backtracking möglich ist. Für diese Klasse von Grammatiksystemen wird der Parsingalgorithmus vorgestellt und die Rolle von Linksableitungen wird detailliert betrachtet.

Title: Derivations of personal names Author: Anna Vanišová Department: Charles University in Prague, Faculty of Arts Study program: Netherlandistics Supervisor: PhDr. Zdenka Hrnčířová Number of pages: 104 Attachments: 45 pages Year: 2011 Key words: derivations, derivatives, suffixes, personal names intuitive forming, productivity This thesis aims to analyze of selected derivations of personal names. Names were chosen to include a range of various suffixes, which are a common base for derivations. The practical part of this work investigates the knowledge and correctness of spontanious intuitive creating of lexicalized derivations of personal names. The research is conducted by questionnaires of Dutch and Czech native speakers.

The paper mainly focuses on legislative deviations from common legislative process in the Czech Republic. For the purpose of comparison it also considers the deviations in Germany and Austria. The derivations are divided into three groups. Firstly, in case of subject derivations the special process rules are reasoned by a specific character of the topic (typically enacting of constitutional or financial law). Secondly, there are accelerating derivations, which are intended to shorten the legislative process. Last but not least, crisis derivations are included. These are used in crisis situations such as war, natural disasters or parliament's incapacity to work. To be more specific, the major section is focused on summary proceedings on law proposals, whereby the position of both parliamentary chambers equals; proceedings on financial law proposals, which are excluded from the voting in the Senate; proceedings on statutory of the Senate measures, which are enacted during the dissolution of the Chamber of deputies; proceedings on law proposals in compliance with the Security Act; law adoption at the first reading, law adoption in the state of legislative emergency, adoption of a law which is connected with a vote of confidence and finally legislative process, which implements the decision of the Security...

Document intends to re-establish Hom-Lie algebra theory for a wider class of morphisms on the underlying coefficient algebra. A look is taken into deformed Witt and Virasoro algebras and a new direction is taken into further quasi-Hom-Lie VIrasoro-type extensions for different Witt algebras.