Dissertations / Theses on the topic 'Jacobson radical'

Neste trabalho consideramos ações parciais torcidas de um grupo G sobre um anel A. Além disso, estudamos ações parciais torcidas que admitem envolvente. No caso em que A e semiprimo, estendemos a ação parcial torcida ao anel de quocientes maximal de A. Com isso, encontramos condições necessárias e suficientes para que o produto cruzado parcial A ∗α G seja um anel semiprimo de Goldie a esquerda. Também, introduzimos o conceito de ação parcial torcida X - externa estudando algumas propriedades que se transferem de A para A ∗α G quando a ação e deste tipo.
In this work we consider twisted partial actions of a group G on a ring A. Firstly we study twisted partial actions with enveloping action. Next we assume that A is semiprime. In this case we extend the twisted partial action to the maximal left rings of quotients of A. Using this we find necessary and suficient conditions for the partial crossed product A ∗α G to be a semiprime Goldie ring. Finally we introduce the concept of the twisted partial action X -outer and study some properties that transfer from A to A ∗α G when the action is of this type.

O objetivo desta dissertação é estudar o radical de Jacobson de anéis de polinômios diferenciais. Mostramos um resultado de M. Ferrero, K. Kishimoro, K. Motose, que mostra que no caso geral, o radical de um anel de polinômios diferenciais é um anel de polinômios diferenciais sobre algum ideal do anel dos coeficientes. Assumindo que o anel dos coeficientes satisfaça uma identidade polinomial, mostramos seguindo B. Madill que este ideal é um ideal nil. Se o anel dos coeficientes é adicionalmente localmente nilpotente, seguindo J. Bell, B. Madill, F. Shinko, mostramos que o anel de polinômios diferenciais será localmente nilpotente. Ainda seguindo J. Bell et al, se o anel dos coeficientes é uma álgebra sobre um corpo de característica zero e tal álgebra satisfaz uma identidade polinomial, mostramos que o ideal nil é o radical de Köthe. Para tais demonstrações, cobriremos os tópicos preliminares necessários para entender os enunciados: radical nil, radical de Levitzki, radical de Baer, radical de Jacobson e propriedades, anéis PI, polinômios centrais, teorema de Kaplansky.
The aim of this work is to study the Jacobson radical of differential polynomial rings. We show a result of M. Ferrero, K. Kishimoto, K. Motose, which shows that in general, the radical of a differential polynomial ring is a differential polynomial ring over some ideal of the ring of coefficients. Assuming that the ring of coefficients satisfies a polynomial identity, we show following B. Madill that this ideal is nil. If the ring of coefficients is additionally locally nilpotent, following J. Bell, B. Madill, F. Shinko, we show that the differential polynomial ring is locally nilpotent. Still following J. Bell et al, if the ring of coefficients is an algebra over a field of zero characteristic and this algebra satisfies a polynomial identity, we show that the nil ideal is the Köthe radical. For the proofs, we cover the preliminary topics necessary for understanding the statements: nil radical, Levitzki radical, Baer radical, Jacobson radical and its properties, PI-rings, central polynomials, Kaplanskys theorem.

The Jacobson radical of a ring was first formally studied in 1945 by Nathan Jacobson and is an important object in modern abstract algebra. The analogous notion of the Jacobson radical for a module is referred to as the radical of a module. The radical of a module is the intersection of all its maximal submodules. In general, the radical of a module is simpler than the module itself and contains important information about the module. The study of the radical of a module often appears as an incidental to other investigations. This thesis represents work towards understanding the radical of a module extension. Given a ring $R$ and $R$-modules $A,B,X$ such that $X$ is an extension of $B$ by $A$ as in the short exact sequence $$0 rightarrow A rightarrow X rightarrow B rightarrow 0 ,$$ we seek to determine properties of the radical of $X$, denoted $rad{X}$. These properties are dependent on the ring $R$ and properties of the modules $A$ and $B$. In this thesis we examine several different types of extensions and discuss a phenomenon in which a non-zero radical implies a split sequence. We work in the context of rings and their ideals. Extensions of abelian groups provide motivation for the results we prove about injectivity of radicals of extensions involving divisible modules and torsion modules. We are able to prove such properties of the radical for extensions of modules over principal ideal domains and Dedekind domains. Expanding upon these cases, we explore a more general construction of an extension and use it to explain our motivating abelian group results. We use the theorems proven about this construction to remark on possible generalizations to other types of rings and modules. We conclude with plans to generalize our statements by translating into terms of infinite matrices and $h$-local rings.

Nessa dissertação, apresentamos os Teoremas de Dualidade de Cohen e Montgomery, [4]. Discutimos também a construção de um contexto de Morita para uma álgebra graduada por um grupo finito. Como aplicação dos resultados desenvolvidos no texto, estudamos a relação entre o radical de Jacobson e o radical de Jacobson graduado de álgebras graduadas, apresentando a solução de Cohen e Montgomery para uma conjectura de Bergman.
In this work, we will present the Cohen and Montgomery's Duality Theorems, [4]. We also discuss the construction of a Morita context to an algebra graded by a nite group. As an application of the results developed in the text, we studied the relations between the Jacobson radical and the graded Jacobson radical of graded algebras, presenting to Cohen and Montgomery's solution for a Bergman's conjecture.

The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and more. Once we reach our destination, we will examine some implications of these theorems. As a fair warning, no ring will be assumed to be commutative, or to have unity. On that note, the reader should be familiar with the basic findings from Group Theory and Ring Theory.

Cette thèse s'attache à décrire des algorithmes qui répondent à des questions provenant de la théorie des anneaux et des modules. Nous restreindrons essentiellement notre étude à des algorithmes déterministes, en temps polynomial, ainsi qu'aux anneaux et modules finis. Le premier des principaux résultats de cette thèse concerne le problème de l'isomorphisme entre modules : nous décrivons deux algorithmes distincts qui, étant donnée un anneau fini R et deux R-modules M et N finis, déterminent si M et N sont isomorphes. S'ils le sont, les deux algorithmes exhibent un tel isomorphisme. De plus, nous montrons comment calculer un ensemble de générateurs de taille minimale pour un module donné, et comment construire des couvertures projectives et des enveloppes injectives. Nous décrivons ensuite des tests mettant en évidence le caractère simple, projectif ou injectif d'un module, ainsi qu'un test constructif de l'existence d'un homomorphisme demodules surjectif entre deux modules finis, l'un d'entre eux étant projectif. Par contraste, nous montrons le résultat négatif suivant : le problème consistant à tester l'existence d'un homomorphisme de modules injectif entre deux modules, l'un des deux étant projectif, est NP-complet.La dernière partie de cette thèse concerne le problème de l'approximation du radical de Jacobson d'un anneau fini. Il s'agit de déterminer un idéal bilatère nilpotent tel que l'anneau quotient correspondant soit \presque" semi-simple. La notion de \semi-simplicité approchée" que nous utilisons est la séparabilité
In this thesis we are interested in describing algorithms that answer questions arising in ring and module theory. Our focus is on deterministic polynomial-time algorithms and rings and modules that are finite. The first main result of this thesis concerns the module isomorphism problem: we describe two distinct algorithms that, given a finite ring R and two finite R-modules M and N, determine whether M and N are isomorphic. If they are, the algorithms exhibit such a isomorphism. In addition, we show how to compute a set of generators of minimal cardinality for a given module, and how to construct projective covers and injective hulls. We also describe tests for module simplicity, projectivity, and injectivity, and constructive tests for existence of surjective module homomorphisms between two finite modules, one of which is projective. As a negative result, we show that the problem of testing for existence of injective module homomorphisms between two finite modules, one of which is projective, is NP-complete. The last part of the thesis is concerned with finding a good working approximation of the Jacobson radical of a finite ring, that is, a two-sided nilpotent ideal such that the corresponding quotient ring is \almost" semisimple. The notion we use to approximate semisimplicity is that of separability

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Neste trabalho serão estudadas as graduações e identidades polinomiais graduadas da álgebra Un(K) das matrizes triangulares superiores n×n sobre um corpo K, o qual será sempre in nito. Primeiramente, será estudado o caso n = 2, para o qual será mostrado que existe apenas uma graduação não trivial e serão descritos as identidades, as codimensões e os cocaracteres graduados. Para o caso n qualquer, serão estudadas as identidades e codimensões graduadas, considerando-se a Zn-graduação natural de Un(K). Finalmente, será apresentada uma classi cação das graduações de Un(K) por um grupo qualquer.
In this work we study the gradings and the graded polynomial identities of the upper n × n triangular matrices algebra Un(K) over a eld K, which is always in nity. The case n = 2 will be rstly studied, for which will be shown that there is only one nontrivial grading and we shall describe the graded identities, codimensions and cocharacters. For the general n case, we shall study graded identities and codimensions, considering the natural Zn-grading of Un(K). Finally, we will present a classi cation of the gradings of Un(K) by any group.

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Capes
Nesta dissertação estudamos as graduações elementares (ou boas graduações) e as identidades polinomiais graduadas correspondentes em álgebras de matrizes triangulares superiores em blocos. Uma graduação elementar por um grupo G na álgebra A = UT(α1, α2, ..., αr) de matrizes triangulares superiores em blocos é determinada por uma n-upla em Gn, onde n = α1+· · ·+αr. Mostraremos que as graduações elementares em A determinadas por duas n-uplas em Gnsão isomorfas se, e somente se, as n-uplas estão na mesma órbita da bi-ação canônica em Gn com o grupo Sα1 × · · · × Sαr agindo à esquerda e G à direita. Em seguida utilizamos estes resultados para mostrar que, sob certas hipóteses (por exemplo, se o grupo G tem ordem prima), duas álgebras de matrizes triangulares superiores em blocos, graduadas pelo grupo G, satisfazem as mesmas identidades graduadas se, e somente se, são isomorfas (como álgebras graduadas).
In this dissertation we study elementary (or good) gradings in upper block triangular matrix algebras and the corresponding graded polynomial identities. An elementary grading by a group G on the algebra A = UT(α1, α2, ..., αr) of upper block triangular matrices is determined by an n-tuple in Gn, where n = α1 + · · · + αr. It will be proved that the elementary gradings on A determined by two n-tuples in Gn are isomorphic if and only if the n-tuples are in the same orbit in the canonical bi-action on Gn with the group Sα1 × · · · × Sαr acting on the left and the group G acting on the right. These results will be used to prove that under suitable hypothesis (for example if the group G has prime order) two upper block triangular matrix algebras, graded by the group G, satisfy the same graded identities if and only if they are isomorphic (as graded algebras).

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Em um anel R, o conjunto de todos os elementos quaserregulares determina o, assim chamado, grupo adjunto G, cuja operação, conhecida como círculo, foi definida por S. Perlis como x_y = x+y+xy: Este trabalho, tem como objetivo determinar a estrutura do grupo adjunto G de um anel finito R e verificar a validade da propriedade do normalizador em anéis de grupo integrais (Nor) com respeito ao grupo geral linear. Explorando a decomposição do anel R em suas pi-componentes, concluímos que G é produto direto dos grupos adjuntos, Gpi , em cada pi-componente Rpi do anel; demonstraremos então, que para cada fator Gpi , o quociente Gpi=pRpi , admite uma decomposição como o produto semidireto (munido da operação círculo) de Jpi=pRpi , em que Jpi é o radical de Jacobson do anel Rpi , por um produto direto de grupos gerais lineares. Uma vez estabelecida esta estrutura, aplicamos técnicas próprias da teoria de anéis de grupo integrais e mostramos a validade de (Nor) para o grupo geral linear, GL(n; Fqi), onde Fqi é um corpo finito e qi = PI n. Provamos que vale (Nor) para cada fator GL(n; Fqi) e portanto concluímos que o produto direto desses fatores, é solução para (Nor).

Soient r un anneau commutatif noetherien et integre admettant un corps de fractions k, g une k-algebre de lie libre de type fini et nilpotente. On generalise certaines etudes deja faites dans le cas ou r = k sur les ideaux de son algebre enveloppante u(g). On montre que u(g) est classiquement localisable, que tout ideal non nul de u(g) verifie la condition a. R. , admet un systeme centralisant de generateurs et une decomposition primaire classique. On montre que g est nilpotente si et seulement si tout ideal non nul a droite (respectivement a gauche) classiquement primaire. Lorsque r est de jacobson on donne une caracterisation des ideaux primitifs et des ideaux rationnels de u(g). Si r est regulier on montre que u(g) est super-regulier et catenaire. Enfin on determine l'enveloppe injective de r en tant que u(g)-bimodule et en tant que u(g) =lim u(g non)j**(n)-module a gauche et a droite, j =u(g)g = gu(g)

Cette thèse étudie un corpus de romans anglais, encore peu étudiés en France et jamais étudiés collectivement, publiés entre 1782 et 1805 par des écrivains et des écrivaines se rattachant par leurs idées et, pour certains, leur militantisme actif, au mouvement radical qui se développe en Angleterre dans la seconde moitié du XVIIIe siècle, s’amplifie et s’organise sous l’impulsion de la Révolution française, puis, sévèrement réprimé par le gouvernement de William Pitt, s’effondre à la fin de la décennie. Cette séquence historique laisse des traces profondes dans l’œuvre des romanciers radicaux, dont beaucoup, comme William Godwin, Mary Wollstonecraft et John Thelwall, sont philosophes ou polémistes avant d’être romanciers et prennent la plume pour défendre les droits de l’homme (et de la femme) dans le débat anglais sur la Révolution française qui oppose Edmund Burke à Thomas Paine. En croisant l’histoire des idées politiques, l’histoire sociale et culturelle du mouvement radical, l’histoire du livre et la narratologie classique, ce travail s’efforce de mettre en lumière la façon dont les romans encodent une certaine idéologie politique dans leurs formes – du discours des locuteurs au format de publication des romans, en passant par leurs narrateurs, leurs intrigues, leurs personnages, leur style et leurs silences signifiants. Un tel examen fait ressortir, plutôt qu’une idéologie radicale unifiée, une tension récurrente entre deux versions, libérale et jacobine, bourgeoise et plébéienne, du radicalisme, dont l’articulation conflictuelle revêt différentes formes d’un auteur à l’autre et d’un terme à l’autre de la période étudiée, à mesure que la réaction conservatrice enterre les espoirs radicaux de réformes
This dissertation examines a corpus of English novels which have been little studied in France as yet and never as a whole. The novels were published between 1782 and 1805 by a group of writers who, by their ideas and in some cases active political commitment, belong to the radical movement which developed in England in the second half of the eighteenth century, gained impetus and structure in the wake of the French Revolution, and collapsed at the end of the decade when faced with repression from the government of William Pitt. Radical novelists, many of whom, like William Godwin, Mary Wollstonecraft and John Thelwall, were philosophers and pamphleteers before they took to novel-writing, flew to the defence of the rights of man (and of the rights of woman) in the revolution controversy which pitted Thomas Paine against Edmund Burke – and their work bears the mark of the rise and demise of the radical movement. Combining intellectual history with classical narratology, book history, and the social and cultural history of radicalism, this dissertation seeks to highlight the way in which political ideology is built into the very forms of the novels – in the characters’ speech and the characters themselves, in the novels’ plot and narration type, in their style and publishing format, as well as in their meaningful silences. Such a study brings to light, rather than a coherent radical ideology, a recurring tension between two versions of radicalism, liberal and jacobin, bourgeois and plebeian, whose partly conflicting conjunction assumes different shapes from one novelist to the other and between the early 1780s and late 1790s, as radical hopes of reform sink under the conservative backlash

The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

碩士
大同大學
應用數學學系(所)
93
Let R be a prime ring and R[x; d] be the skew polynomial ring over R with a derivation d. We prove two results in this thesis： 1. If R has no nonzero nil ideals and the center of R[x; d] has a nonconstant polynomial, then the Jacobson radical of R[x; d] is zero. 2. If R has no nonzero nil ideals and there is a nonzero ideal of R[x; d] such that �x R = 0, then the Jacobson radical of R[x; d] is also zero.

碩士
大同大學
應用數學研究所
93
Let R be a prime ring and R[x; d] be the skew polynomial ring over R with a derivation d. We prove two results in this thesis： 1. If R has no nonzero nil ideals and the center of R[x; d] has a nonconstant polynomial, then the Jacobson radical of R[x; d] is zero. 2. If R has no nonzero nil ideals and there is a nonzero ideal of R[x; d] such that  R = 0, then the Jacobson radical of R[x; d] is also zero.

by Au Yun-Nam.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.
Includes bibliographical references (leaves 133-137).
Introduction --- p.iv
Chapter 1 --- Preliminaries --- p.1
Chapter 1.1 --- Some Semigroup Properties --- p.1
Chapter 1.2 --- General Properties of Semigroup Algebras --- p.5
Chapter 1.3 --- Group Algebras --- p.7
Chapter 1.3.1 --- Some Basic Properties of Groups --- p.7
Chapter 1.3.2 --- General Properties of Group Algebras --- p.8
Chapter 1.3.3 --- Δ-Method for Group Algebras --- p.10
Chapter 1.4 --- Graded Algebras --- p.12
Chapter 1.5 --- Crossed Products and Smash Products --- p.14
Chapter 2 --- Radicals of Graded Rings --- p.17
Chapter 2.1 --- Jacobson Radical of Crossed Products --- p.17
Chapter 2.2 --- Graded Radicals and Reflected Radicals --- p.18
Chapter 2.3 --- Radicals of Group-graded Rings --- p.24
Chapter 2.4 --- Algebras Graded by Semilattices --- p.26
Chapter 2.5 --- Algebras Graded by Bands --- p.27
Chapter 2.5.1 --- Hereditary Radicals of Band-graded Rings --- p.27
Chapter 2.5.2 --- Special Band-graded Rings --- p.30
Chapter 3 --- Radicals of Semigroup Algebras --- p.34
Chapter 3.1 --- Radicals of Polynomial Rings --- p.34
Chapter 3.2 --- Radicals of Commutative Semigroup Algebras --- p.36
Chapter 3.2.1 --- Commutative Cancellative Semigroups --- p.37
Chapter 3.2.2 --- General Commutative Semigroups --- p.39
Chapter 3.2.3 --- The Nilness and Semiprimitivity of Commutative Semigroup Algebras --- p.45
Chapter 3.3 --- Radicals of Cancellative Semigroup Algebras --- p.48
Chapter 3.3.1 --- Group of Fractions of Cancellative Semigroups --- p.48
Chapter 3.3.2 --- Jacobson Radical of Cancellative Semigroup Algebras --- p.54
Chapter 3.3.3 --- Subsemigroups of Polycyclic-by-Finite Groups --- p.57
Chapter 3.3.4 --- Nilpotent Semigroups --- p.59
Chapter 3.4 --- Radicals of Algebras of Matrix type --- p.62
Chapter 3.4.1 --- Properties of Rees Algebras --- p.62
Chapter 3.4.2 --- Algebras Graded by Elementary Rees Matrix Semigroups --- p.65
Chapter 3.5 --- Radicals of Inverse Semigroup Algebras --- p.68
Chapter 3.5.1 --- Properties of Inverse Semigroup Algebras --- p.69
Chapter 3.5.2 --- Radical of Algebras of Clifford Semigroups --- p.72
Chapter 3.5.3 --- Semiprimitivity Problems of Inverse Semigroup Algebras --- p.73
Chapter 3.6 --- Other Semigroup Algebras --- p.76
Chapter 3.6.1 --- Completely Regular Semigroup Algebras --- p.76
Chapter 3.6.2 --- Separative Semigroup Algebras --- p.77
Chapter 3.7 --- Radicals of Pi-semigroup Algebras --- p.80
Chapter 3.7.1 --- PI-Algebras --- p.80
Chapter 3.7.2 --- Permutational Property and Algebras of Permutative Semigroups --- p.80
Chapter 3.7.3 --- Radicals of PI-algebras --- p.82
Chapter 4 --- Finiteness Conditions on Semigroup Algebras --- p.85
Chapter 4.1 --- Introduction --- p.85
Chapter 4.1.1 --- Preliminaries --- p.85
Chapter 4.1.2 --- Semilattice Graded Rings --- p.86
Chapter 4.1.3 --- Group Graded Rings --- p.88
Chapter 4.1.4 --- Groupoid Graded Rings --- p.89
Chapter 4.1.5 --- Semigroup Graded PI-Algebras --- p.91
Chapter 4.1.6 --- Application to Semigroup Algebras --- p.92
Chapter 4.2 --- Semiprime and Goldie Rings --- p.92
Chapter 4.3 --- Noetherian Semigroup Algebras --- p.99
Chapter 4.4 --- Descending Chain Conditions --- p.107
Chapter 4.4.1 --- Artinian Semigroup Graded Rings --- p.107
Chapter 4.4.2 --- Semilocal Semigroup Algebras --- p.109
Chapter 5 --- Dimensions and Second Layer Condition on Semigroup Algebras --- p.119
Chapter 5.1 --- Dimensions --- p.119
Chapter 5.1.1 --- Gelfand-Kirillov Dimension --- p.119
Chapter 5.1.2 --- Classical Krull and Krull Dimensions --- p.121
Chapter 5.2 --- The Growth and the Rank of Semigroups --- p.123
Chapter 5.3 --- Dimensions on Semigroup Algebras --- p.124
Chapter 5.4 --- Second Layer Condition --- p.128
Notations and Abbreviations --- p.132
Bibliography --- p.133

Rozprawa ta poświęcona jest badaniu półgrupy C(A) klas sprzężoności ideałów lewostronnych skończenie wymiarowej algebry A z 1 nad ciałem K. Mnożenie w tej półgrupie pochodzi w sposób naturalny od struktury multyplikatywnej samej algebry. Wykazano szereg rezultatów dotyczących struktury C(A). Udowodniono, że skończoność C(A) równoważna jest temu, że liczba klas sprzężoności lewostronnych ideałów nilpotentnych algebry A jest skończona. Wskazano pewne niezmienniki algebry A, które można odczytać ze struktury półgrupy C(A). Przy założeniu, że K jest algebraicznie domknięte oraz, że radykał Jacobsona algebry A jest 2-nilpotentny wykazano, że struktura półgrupy C(A) determinuje strukturę algebry A, przy dodatkowym założeniu, że C(A) jest skończona. W kontekście rozważanej w tym rezultacie klasy algebr, uzyskano także pewne częściowe wyniki związane z opisem algebr, w których półgrupa klas sprzężoności jest skończona. Pokazano, między innymi, że jeśli A jest algebrą z 2-nilpotentnym radykałem Jacobsona, wówczas skończoność półgrupy C(M_6(A)) równoważna jest temu, że A ma skończony typ reprezentacyjny.
The aim of this thesis is to investigate the semigroup C(A) of conjugacy classes of left ideals of a finite dimensional algebra A with 1 over a field K. The operation in this semigroup is naturally induced from the multiplicative structure of the algebra itself. We determine certain invariants of an algebra A that can be expressed in terms of the structure of C(A). Assuming that the field K is algebraically closed and that the Jacobson radical of the algebra A is 2-nilpotent, we prove that the structure of the semigroup C(A) completely determines the structure of A, assuming that C(A) is finite. In the context of the class of algebras that are considered for this result, some partial results concerning the classification of algebras for which the semigroups of conjugacy classes are finite are obtained. It is shown, among other results, that if the algebra A has 2-nilpotent Jacobson radical then the finiteness of C(M_6(A)) is equivalent to the fact, that A is of finite representation type.

Student Number : 8315331 - MSc dissertation - School of Electrical and Information Engineering - Faculty of Engineering and the Built Environment
In this dissertation an efficient algorithm to calculate the differential of the network output with respect to its inputs is derived for axis orthogonal Local Model (LMN) and Radial Basis Function (RBF) Networks. A new recursive Singular Value Decomposition (SVD) adaptation algorithm, which attempts to circumvent many of the problems found in existing recursive adaptation algorithms, is also derived. Code listings and simulations are presented to demonstrate how the algorithms may be used in on-line adaptive neurocontrol systems. Specifically, the control techniques known as series inverse neural control and instantaneous linearization are highlighted. The presented material illustrates how the approach enhances the flexibility of LMN networks making them suitable for use in both direct and indirect adaptive control methods. By incorporating this ability into LMN networks an important characteristic of Multi Layer Perceptron (MLP) networks is obtained whilst retaining the desirable properties of the RBF and LMN approach.