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Dissertations / Theses on the topic 'Units in rings and group rings'

Author: Grafiati

Published: 6 September 2023

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1

Li, Yuanlin. "Units in integral group rings." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/nq23107.pdf.

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2

Ferguson, Ronald Aubrey. "Units in integral cyclic group rings for order L§RP§S." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25045.pdf.

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3

Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/368142.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie alg

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4

Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, University of Trento, 2014. http://eprints-phd.biblio.unitn.it/1182/1/PhdThesisFaccinPaolo.pdf.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie alg

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5

Silva, Renata Rodrigues Marcuz. "Unidades de ZC2p e Aplicações." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-27062012-154612/.

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Seja p um número primo e seja uma raiz p - ésima primitiva da unidade. Considere os seguintes elementos i := 1 + + 2 + ... + i-1 para todo 1 i k do anel Z[] onde k = (p-1)/2. Nesta tese nós descrevemos explicitamente um conjunto gerador para o grupo das unidades do anel de grupo integral ZC2p; representado por U(ZC2p); onde C2p representa o grupo cíclico de ordem 2p e p satisfaz as seguintes condições: S := { -1, , u2, ... uk } gera U(Z[]) e U(Zp) = ou U(Zp)2 = e -1 U(Zp); que são verificadas para p = 7; 11; 13; 19; 23; 29; 53; 59; 61 e 67. Com o intuito de estender tais ideias encont

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6

Kitani, Patricia Massae. "Unidades de ZCpn." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-26042012-235529/.

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Seja Cp um grupo cíclico de ordem p, onde p é um número primo tal que S = {1, , 1+\\theta, 1+\\theta+\\theta^2, · · · , 1 +\\theta + · · · + \\theta ^{p-3/2}} gera o grupo das unidades de Z[\\theta] e é uma raiz p-ésima primitiva da unidade sobre Q. No artigo \"Units of ZCp\" , Ferraz apresentou um modo simples de encontrar um conjunto de geradores independentes para o grupo das unidades do anel de grupo ZCp sobre os inteiros. Nós estendemos este resultado para ZCp^n , considerando que um conjunto similar a S gera o grupo das unidades de Z[\\theta]. Isto ocorre, por exemplo, quando \\phi

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7

Stack, Cora. "Some results on the structure of the groups of units of finite completely primary rings and on the structure of finite dimensional nilpotent algebras." Thesis, University of Reading, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262483.

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8

Filho, Antonio Calixto de Souza. "A importância das unidades centrais em anéis de grupo." Universidade de São Paulo, 2000. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-11122008-214317/.

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Na presente dissertação, discutimos o Problema do Isomorfismo em anéis de grupo para grupos infinitos da forma G × C, apresentado no artigo de Mazur [14], que enuncia um teorema mostrando a equivalência para o Problema do Isomorfismo entre essa classe de grupos infinitos e grupos finitos que satisfaçam a Conjectura do Normalizador. Nossa ênfase concentra-se na relação entre a Conjectura do Isomorfismo e a Conjectura do Normalizador, primeiramente, observada nesse artigo. Em seguida, consideramos um teorema de estrutura para as unidades centrais em anéis de grupo comunicado, pela primeira vez,

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9

Immormino, Nicholas A. "Clean Rings & Clean Group Rings." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1374247918.

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10

Weber, Harald. "Group rings and twisted group rings for a series of p-groups." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10761310.

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11

Turner, Emma Louise. "k-S-Rings." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3670.

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For a finite group G we study certain rings called k-S-rings, one for each non-negative integer k, where the 1-S-ring is the centralizer ring of G. These rings have the property that the (k+1)-S-ring determines the k-S-ring. We show that the 4-S-ring determines G when G is any group with finite classes. We show that the 3-S-ring determines G for any finite group G, thus giving an answer to a question of Brauer. We show the 2-characters defined by Frobenius and the extended 2-characters of Ken Johnson are characters of representations of the 2-S-ring of G. We find the character table for the 2-

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12

Dexter, Cache Porter. "Schur Rings over Infinite Groups." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8831.

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A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.

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13

Srivastava, Ashish K. "Rings Characterized by Properties of Direct Sums of Modules and on Rings Generated by Units." Ohio University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1181845354.

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14

Strouthos, I. "Stably free modules over group rings." Thesis, University College London (University of London), 2011. http://discovery.ucl.ac.uk/1325632/.

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We study finitely generated stably free modules over group rings associated to particular groups, primarily using Milnor’s construction of projective modules over rings and Quillen’s Patching Theorem. For an odd prime number q, we study the stably free module category of the group ring of the dihedral group of order 2q over the ring of integer coefficient polynomials in one variable. We show that, over this group ring, every stably free module is free if every stably free module is free over a particular localisation of a cyclic algebra over the ring of algebraic integers corresponding to the

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15

Welch, Amanda Renee. "Characterizing Zero Divisors of Group Rings." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52949.

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The Atiyah Conjecture originates from a paper written 40 years ago by Sir Michael Atiyah, a famous mathematician and Fields medalist. Since publication of the paper, mathematicians have been working to solve many questions related to the conjecture, but it is still open. The conjecture is about certain topological invariants attached to a group G. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group. We are interested in looking at examples where this is not the case. We are interested in the specific case where G

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16

Archer, Louise. "Hall algebras and Green rings." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:960af4b3-8f32-4263-9142-261f49d52405.

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This thesis consists of two parts, both of which involve the study of algebraic structures constructed via the multiplication of modules. In the first part we look at Hall algebras. We consider the Hall algebra of a cyclic quiver algebra with relations of length two and present a multiplication formula for the explicit calculation of products in this algebra. We then look at the case of a cyclic quiver with two vertices and describe the corresponding composition algebra as a quotient of the positive part of a quantised enveloping algebra of type Ã<sub>1</sub> We then look at quotients of Hall

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17

Kahn, Eric B. "THE GENERALIZED BURNSIDE AND REPRESENTATION RINGS." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/707.

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Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module is known as the linearizati

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18

邵慰慈 and Wai-chee Shiu. "The algebraic structure and computation of Schur rings." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31233181.

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19

Shiu, Wai-chee. "The algebraic structure and computation of Schur rings /." [Hong Kong : University of Hong Kong], 1992. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1329037X.

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20

Meyer, David Christopher. "Universal deformation rings and fusion." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1883.

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This thesis is on the representation theory of finite groups. Specifically, it is about finding connections between fusion and universal deformation rings. Two elements of a subgroup N of a finite group Γ are said to be fused if they are conjugate in Γ, but not in N. The study of fusion arises in trying to relate the local structure of Γ (for example, its subgroups and their embeddings) to the global structure of Γ (for example, its normal subgroups, quotient groups, conjugacy classes). Fusion is also important to understand the representation theory of Γ (for example, through the formula for

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21

Lee, Gregory Thomas. "Symmetric elements in group rings and related problems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59994.pdf.

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22

Gjerling, Andreas. "On rings of quotients of soluble group algebras." Thesis, Queen Mary, University of London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286813.

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23

Alahmadi, Adel Naif M. "Injectivity, Continuity, and CS Conditions on Group Rings." Ohio University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1163521064.

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24

Mannan, W. H. "Low dimensional algebraic complexes over integral group rings." Thesis, University College London (University of London), 2007. http://discovery.ucl.ac.uk/1446153/.

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The realization problem asks: When does an algebraic complex arise, up to homotopy, from a geometric complex In the case of 2- dimensional algebraic complexes, this is equiv alent to the D2 problem, which asks when homological methods can distinguish between 2 and 3 dimensional complexes. We approach the realization problem (and hence the D2 problem) by classifying all pos sible algebraic 2- complexes and showing that they are realized. We show that if a dihedral group has order 2n, then the algebraic complexes over it are parametrized by their second homology groups, which we refer to as alge

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25

Kerby, Brent L. "Rational Schur Rings over Abelian Groups." BYU ScholarsArchive, 2008. https://scholarsarchive.byu.edu/etd/1491.

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In 1993, Muzychuk showed that the rational S-rings over a cyclic group Z_n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z_n. This idea is easily extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational S-rings over G in a natural way. Our main result is that any finite group may be represented as the automorphism group of such a rational S-ring over an abelian p-group. In order to show this, we first give a complete descriptio

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26

邵慰慈 and Wai-chee Shiu. "Schur rings over dihedral groups of order 2p." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31208873.

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27

Shiu, Wai-chee. "Schur rings over dihedral groups of order 2p /." [Hong Kong : University of Hong Kong], 1989. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12364770.

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28

Eisele, Florian [Verfasser]. "Group rings over the p-Adic integers / Florian Eisele." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1022616773/34.

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29

Ahmed, Iftikhar. "Projective modules of group rings over quadratic number fields." Thesis, Durham University, 1994. http://etheses.dur.ac.uk/5669/.

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Let K be a quadratic number field, Ok its ring of integers, and G a cyclic group of order prime p. In this thesis, we study the kernel group D(O(_K)G) and obtain a number of results concerning its order and structure. For K imaginary, we also investigate the subset R(O(_k)G) of the locally free class group CI(O(_k)G) consisting of classes which occur as rings of integers of tame extensions of K with Galois group isomorphic to G. We calculate R(O(_k)G) under a variety of conditions and obtain, for an arbitrary tame extension L o( K with group G, invariants which determine the class of O(_L) in

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30

DOROBISZ, KRZYSZTOF. "INVERSE PROBLEMS FOR UNIVERSAL DEFORMATION RINGS OF GROUP REPRESENTATIONS." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/268872.

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We study representations of profinite groups over some particular type of local rings. More specifically, suppose a profinite group and its continuous finite dimensional representation over a finite field k are given. Then we are interested in studying all possibilities of lifting this representation to a representation over a ring that is complete, local, noetherian and whose residue field is isomorphic to k. For each problem of the above described type, an associated deformation functor can be defined. If such a functor is representable then the object representing it is called the univer

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31

Juglal, Shaanraj. "Prime near-ring modules and their links with the generalised group near-ring." Thesis, Nelson Mandela Metropolitan University, 2007. http://hdl.handle.net/10948/714.

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In view of the facts that the definition of a ring led to the definition of a near- ring, the definition of a ring module led to the definition of a near-ring module, prime rings resulted in investigations with respect to primeness in near-rings, one is naturally inclined to attempt to define the notion of a group near-ring seeing that the group ring had already been defined and investigated into by, interalia, Groenewald in [7] . However, in trying to define the group near-ring along the same lines as the group ring was defined, it was found that the resulting multiplication was, in general,

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32

Semikina, Iuliia [Verfasser]. "G-theory of group rings for finite groups / Iuliia Semikina." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1173789642/34.

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33

Tay, Julian Boon Kai. "Poincaré Polynomial of FJRW Rings and the Group-Weights Conjecture." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3604.

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FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is define

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34

Renshaw, James Henry. "Flatness, extension and amalgamation in monoids, semigroups and rings." Thesis, University of St Andrews, 1986. http://hdl.handle.net/10023/11071.

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We begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in the category of S-sets. Chapter II introduces the important concept of free extensions and uses this to describe the amalgamated free product. In Chapter III we define the extension property and the notion of purity. We show that many of the important notions in semigroup amalgams are intimately connected to these. In Section 2 we deduce that 'the extension property implies am

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35

Lännström, Daniel. "The structure of epsilon-strongly graded rings with applications to Leavitt path algebras and Cuntz-Pimsner rings." Licentiate thesis, Blekinge Tekniska Högskola, Institutionen för matematik och naturvetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-17809.

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The research field of graded ring theory is a rich area of mathematics with many connections to e.g. the field of operator algebras. In the last 15 years, algebraists and operator algebraists have defined algebraic analogues of important operator algebras. Some of those analogues are rings that come equipped with a group grading. We want to reach a better understanding of the graded structure of those analogue rings. Among group graded rings, the strongly graded rings stand out as being especially well-behaved. The development of the general theory of strongly graded rings was initiated by Dad

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36

Popov, Vladimir L., and vladimir@popov msk su. "Generators and Relations of the Affine Coordinate Rings of Connected." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi972.ps.

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37

Pilewski, Nicholas J. "Units and Leavitt Path Algebras." Ohio University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1427464498.

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38

Grover, Parnesh Kumar Carleton University Dissertation Mathematics. "Orderings on division rings and normal subgroup structure of a unitary group." Ottawa, 1989.

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39

Nguyen, Long Pham Bao. "Fusion of Character Tables and Schur Rings of Dihedral Groups." BYU ScholarsArchive, 2008. https://scholarsarchive.byu.edu/etd/1429.

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A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We investigate the case where H is the dihedral group. In many cases, G can be completely determined. In general, G can be proven to have many interesting properties. The theory is developed in terms of S-ring of Schur and Wielandt.

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40

Helveston, John Knox. "Life rings a manual for developing small group ministry in an established church /." Theological Research Exchange Network (TREN), 1997. http://www.tren.com.

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41

Harris, Julianne S. "On the mod 2 general linear group homology of totally real number rings /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5812.

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42

Szabo, Steve. "Convolutional Codes with Additional Structure and Block Codes over Galois Rings." Ohio University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1257792383.

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43

Köster, Iris [Verfasser], and Wolfgang [Akademischer Betreuer] Kimmerle. "Sylow numbers in character tables and integral group rings / Iris Köster ; Betreuer: Wolfgang Kimmerle." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2017. http://d-nb.info/1130148572/34.

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44

Bächle, Andreas [Verfasser], and Wolfgang [Akademischer Betreuer] Kimmerle. "On torsion subgroups and their normalizers in integral group rings / Andreas Bächle. Betreuer: Wolfgang Kimmerle." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2013. http://d-nb.info/1029460787/34.

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45

Long, Jane Holsapple. "The cohomology rings of the special affine group of Fp^2 and of PSL(3,p)." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8458.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.<br>Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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46

Gandhi, Raj. "Oriented Cohomology Rings of the Semisimple Linear Algebraic Groups of Ranks 1 and 2." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42566.

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In this thesis, we compute minimal presentations in terms of generators and relations for the oriented cohomology rings of several semisimple linear algebraic groups of ranks 1 and 2 over algebraically closed fields of characteristic 0. The main tools we use in this thesis are the combinatorics of Coxeter groups and formal group laws, and recent results of Calm\`es, Gille, Petrov, Zainoulline, and Zhong, which relate the oriented cohomology rings of flag varieties and semisimple linear algebraic groups to the dual of the formal affine Demazure algebra.

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47

Sommerhäuser, Yorck. "Yetter-Drinfel'd-Hopf algebras over groups of prime order /." Berlin [u.a.] : Springer, 2002. http://www.loc.gov/catdir/enhancements/fy0817/2002070799-d.html.

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48

Pitt, Melanie A. 1980. "Main group supramolecular coordination chemistry: Design strategies and dynamic assemblies." Thesis, University of Oregon, 2009. http://hdl.handle.net/1794/10287.

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xxi, 172 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>Main group supramolecular chemistry is a rapidly expanding field that combines the tools of coordination chemistry with the unusual and frequently unexpected coordination preferences exhibited by the main group elements. Application of established supramolecular design principles to those elements provides access to novel structure types and the possibility of new functionality introduced by the rich chemistry of the main group.

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49

Iwaki, Edson Ryoji Okamoto. "Unidades Hipercentrais em Anéis de Grupo." Universidade de São Paulo, 2000. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-20052007-112821/.

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Grande parte dos problemas em Anéis de Grupo centraliza-se em torno do estudo do seu grupo de unidades. Torna-se importante então conhecermos a estrutura do grupo de unidades de um anel de grupo U(ZG). No entanto, salvo raras exceções, pouco se conhece acerca da estrutura de U(ZG). Uma das idéias para se conhecer um pouco mais sobre a estrutura do grupo de unidades seria estudarmos a sua série central superior. No caso em que o grupo G é finito, um resultado de Gruenberg pode ser usado para mostrar que a série central superior de U = U(ZG) estaciona. Este fato nos possibilita estuda

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50

Pallekonda, Seshendra. "Bounded category of an exact category." Diss., Online access via UMI:, 2008.

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