For many matrix algebras, every associative automorphism is inner. We discuss results by Đoković that a non-associative Lie automorphism φ of a triangular matrix algebra Tₙ over a connected unital commutative ring, is of the form φ(A)=SAS⁻¹ + τ(A)I or φ(A)=−SJ Aᵀ JS⁻¹ + τ(A)I, where S ∈ Tₙ is invertible, J is an antidiagonal permutation matrix, and τ is a generalized trace. We incorporate additional arguments by Cao that extended Đoković’s result to unital commutative rings containing nontrivial idempotents. Following this we develop new results for Lie isomorphisms of block upper-triangular matrix algebras over unique factorization domains. We build on an approach used by Marcoux and Sourour to characterize Lie isomorphisms of nest algebras over separable Hilbert spaces. We find that these Lie isomorphisms generally follow the form φ = σ + τ where σ is either an associative isomorphism or the negative of an associative anti-isomorphism, and τ is an additive mapping into the center, which maps commutators to zero. This echoes established results by Martindale for simple and prime rings. / Graduate

In this dissertation the Bays-Lambossy theorem is generalized to GF(pn). The Bays-Lambossy theorem states that if two Cayley objects each based on GF(p) are isomorphic then they are isomorphic by a multiplier map. We use this characterization to show that under certain conditions two isomorphic Cayley objects over GF(pn) must be isomorphic by a function on GF(pn) of a particular type.

Submitted by Elba Lopes (elba.lopes@fecap.br) on 2016-12-02T21:48:13Z No. of bitstreams: 2 Vlademir Betaressi.pdf: 1019882 bytes, checksum: 7be2d1171569df7c08af89e64bf47c6f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-12-02T21:48:13Z (GMT). No. of bitstreams: 2 Vlademir Betaressi.pdf: 1019882 bytes, checksum: 7be2d1171569df7c08af89e64bf47c6f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-09-05 / The isomorphism approach assumes that organizations respond in similar ways to other organizations when these are adjusted to a particular environment. The Comptroller, in the current economic context, plays the role of generating information in order to tailor this information to the company profile and managers that it will use in business management. The speed of business together with the competitiveness between companies makes assignments and controllership practices to grow, in a relevant way, in organizations. The research proposed in this study aimed to analyze the evidence of isomorphism in Controllership practices in companies in the private concessionaires segment of public water and sewage services. This segment has different characteristics from the others, with a strong regulation of their activities, their main duties and responsibilities are clearly defined in the contract and need to follow to the letter these settings to be avoided contractual disputes that may lead to the maximum penalty of suspension of the contract . These rights and obligations are, for example, the definition of the tariff value, the value of investments, the percentage of return on investments, all of which impact significantly on the dealership's management, making the performance of the more relevant controllership within these organizations. The methodology consists of a descriptive research with a qualitative approach, whose data were collected through interviews with semi-structured. The interviews were carried out with the responsible for the financial department of two major business groups, industry-leading group of construction and holders of various assets in the utilities sector, among these, in the sanitation sector, specifically water and sewage, which also have expression of participation of these assets. The research identified as finding evidence of coercive isomorphism, caused primarily by pressures of the concession agreement and the holding of these utilities. Also identified evidence of mimetic isomorphism, the controllership practices of dealers and their structures and, finally, noted the normative isomorphism in only one of the companies searched. It was concluded that there is evidence of three types of isomorphism in the practices of controlling the private concessionaires of public water and sewage services, and these aren't related to each other or are independent. / A abordagem do isomorfismo pressup??e que as organiza????es respondam de maneiras similares a outras organiza????es, quando essas est??o ajustadas a um determinado ambiente. A Controladoria, dentro do contexto econ??mico atual, exerce o papel de geradora de informa????o, de maneira a adequar tal informa????o ao perfil da empresa e dos gestores que dela far??o uso na gest??o dos neg??cios. A velocidade dos neg??cios aliada ?? competitividade entre as empresas faz com que as atribui????es e pr??ticas de controladoria cres??am, de modo relevante, nas organiza????es. A pesquisa proposta neste estudo objetivou analisar as evid??ncias do isomorfismo nas pr??ticas de Controladoria nas empresas do segmento de concession??rias privadas de servi??os p??blicos de ??gua e esgoto. Esse segmento possui caracter??sticas diferenciadas dos demais, apresentando uma forte regulamenta????o de suas atividades, seus principais direitos e responsabilidades s??o claramente definidos em contrato e necessitam seguir ?? risca essas defini????es para que sejam evitados lit??gios contratuais que podem levar at?? ?? penalidade m??xima de suspens??o do contrato. Entre esses direitos e obriga????es est??o, por exemplo, a defini????o do valor da tarifa, os valores dos investimentos, os percentuais de retorno do investimentos, aspectos que impactam significativamente na gest??o da concession??ria, tornando a atua????o da controladoria ainda mais relevante dentro dessas organiza????es. A metodologia utilizada consiste em uma pesquisa descritiva com abordagem qualitativa, cujos dados foram coletados por meio de entrevistas com roteiro semiestruturado e an??lise documental. As entrevistas foram aplicadas junto aos respons??veis pela controladoria de dois grandes grupos empresariais, grupos l??deres do segmento da constru????o civil e detentores de diversos ativos no segmento de concession??rias, entre esses, no segmento de saneamento, especificamente ??gua e esgoto, no qual tamb??m possuem express??o de participa????o desses ativos. A pesquisa identificou como achado evid??ncias do isomorfismo coercitivo, ocasionado basicamente por press??es do contrato de concess??o e pela holding dessas concession??rias. Identificou, tamb??m, evid??ncias do isomorfismo mim??tico, nas pr??ticas de controladoria das concession??rias e nas suas estruturas e, por fim, observou o isomorfismo normativo em apenas uma das empresas pesquisada. Concluiu-se que existem evid??ncias dos tr??s tipos de isomorfismo nas pr??ticas de controladoria das concession??rias privadas de servi??os p??blicos de ??gua e esgoto, sendo que esses n??o est??o relacionados entre si ou s??o independentes.

by Lok Tsan-ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 74-75). / Introduction --- p.2 / Chapter 1 --- "Rings, Modules and Categories" --- p.4 / Chapter 1.1 --- "Rings, Subrings and Ideals" --- p.5 / Chapter 1.2 --- Modules and Categories --- p.8 / Chapter 1.3 --- Module Theory --- p.13 / Chapter 2 --- Isomorphisms between Endomorphism rings of Quasiprogener- ators --- p.24 / Chapter 2.1 --- Preliminaries --- p.24 / Chapter 2.2 --- The Fundamental Theorem --- p.31 / Chapter 2.3 --- Isomorphisms Induced by Semilinear Maps --- p.41 / Chapter 2.4 --- Isomorphisms of General linear groups --- p.46 / Chapter 3 --- Endomorphism ring of projective module --- p.54 / Chapter 3.1 --- Preliminaries --- p.54 / Chapter 3.2 --- Main Theorem --- p.60 / Bibliography --- p.74

Graph Isomorphism is one of the very few classical problems in NP of unsettled complexity status. The families of highly regular structures, for example Steiner 2-designs, strongly regular graphs and primitive coherent configurations, have been perceived as difficult cases for graph isomorphism. These highly regular structures arise naturally as obstacles for both the classical group theory and combinatorial approaches for the graph isomorphism problem. In this thesis we investigate the isomorphism problem of highly regular structures. We present new results to understand the combinatorial structure of highly regular structures, and propose some new algorithms to compute the canonical forms (and thus isomorphism testing) of highly regular structures based on the structural theorems. We also give an algorithm solving the isomorphism problem of two unknown graphs in the property testing setting. Our new algorithm has sample complexity matching the information theoretical lower bound up to some multiplicative subpolynomial factor.

Thesis (Ph.D.)--Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

The purpose of this project was to study the classical result in this direction discovered by O. Ore in 1938, as well as related theorems and corollaries. Ore's Theorem and its corollaries provide us with several results relating distributive lattices with cyclic groups.

The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.

We investigate weak Cayley table isomorphisms, a generalization of group isomorphisms. Suppose G and H are groups. A bijective map phi : G to H is a weak Cayley table isomorphism if it satisfies two conditions:(1) If x is conjugate to y, then phi(x) is conjugate to phi(y); (2) For all x, y in G, phi(xy) is conjugate to phi(x)phi(y).If there exists a weak Cayley table isomorphism between two groups, then we say that the two groups have the same weak Cayley table.This dissertation has two main goals. First, we wish to find sufficient conditions under which two groups have the same weak Cayley table. We specifically study Frobenius groups and groups which satisfy the Camina pair condition. Second, we consider the group of all weak Cayley table isomorphisms between G and itself. We call this group the weak Cayley table group of G and denote it by W(G). Any automorphism of G is an element of W. The inverse map on G is also an element of W. We say that the weak Cayley table group is trivial if it is generated by the set of all automorphisms of G and the inverse map. Stephen Humphries proved that the symmetric groups S_n, the dihedral groups D_{2n} and the free groups F_n (n not equal to 3) all have trivial weak Cayley table groups. We will investigate the weak Cayley table groups of the alternating groups, certain types of Coxeter groups, the projective special linear groups and certain sporadic simple groups.

This dissertation deals with three topics in descriptive set theory. First, the order topology is a natural topology on ordinals. In Chapter 2, a complete classification of order topologies on ordinals up to Borel isomorphism is given, answering a question of Benedikt Löwe. Second, a map between separable metrizable spaces X and Y preserves complete metrizability if Y is completely metrizable whenever X is; the map is resolvable if the image of every open (closed) set in X is resolvable in Y. In Chapter 3, it is proven that resolvable maps preserve complete metrizability, generalizing results of Sierpiński, Vainštein, and Ostrovsky. Third, an equivalence relation on a Polish space has the Laczkovich-Komjáth property if the following holds: for every sequence of analytic sets such that the limit superior along any infinite set of indices meets uncountably many equivalence classes, there is an infinite subsequence such that the intersection of these sets contains a perfect set of pairwise inequivalent elements. In Chapter 4, it is shown that every coanalytic equivalence relation has the Laczkovich-Komjáth property, extending a theorem of Balcerzak and Głąb.