scholarly journals Gorenstein in codimension 4: the general structure theory

2019 ◽  
Author(s):  
Miles Reid
Keyword(s):  
General Structure ◽  
Structure Theory

scholarly journals Free bands and free *-bands

1986 ◽  
Vol 28 (2) ◽  
pp. 161-179 ◽  
Author(s):  
J. A. Gerhard ◽  
Mario Petrich
Keyword(s):  
Word Problem ◽  
Early Paper ◽  
General Structure ◽  
Structure Theory ◽  
Free Band

The word problem for free bands (idempotent semigroups) was solved by Green and Rees [4] in an early paper. They also established certain properties of the free band. This was followed by McLean [6] who provided a general structure theory for bands with some indication as to the structure of the free band. Since then a great many papers have appeared dealing with various aspects of the topic of bands and their varieties. A different solution of the word problem for free bands was recently given by Siekmann and Szabó [9]. For a discussion of bands, see the books [5] and [8].

RECONSTRUCTING GROUP ACTIONS

2013 ◽  
Vol 23 (02) ◽  
pp. 255-323
Author(s):  
LISA CARBONE ◽  
ELIYAHU RIPS
Keyword(s):  
General Structure ◽  
Group Actions ◽  
Free Action ◽  
Universal Covering ◽  
Structure Theory ◽  
Local Data ◽  
Graph Of Groups ◽  
Discontinuous Group ◽  
Abstract Group ◽  
Generators And Relations

We give a general structure theory for reconstructing non-trivial group actions on sets without any further assumptions on the group, the action, or the set on which the group acts. Using certain "local data" [Formula: see text] from the action we build a group [Formula: see text] of the data and a space [Formula: see text] with an action of [Formula: see text] on [Formula: see text] that arise naturally from the data [Formula: see text]. We use these to obtain an approximation to the original group G, the original space X and the original action G × X → X. The data [Formula: see text] is distinguished by the property that it may be chosen from the action locally. For a large enough set of local data [Formula: see text], our definition of [Formula: see text] in terms of generators and relations allows us to obtain a presentation for the group G. We demonstrate this on several examples. When the local data [Formula: see text] is chosen from a graph of groups, the group [Formula: see text] is the fundamental group of the graph of groups and the space [Formula: see text] is the universal covering tree of groups. For general non-properly discontinuous group actions our local data allows us to imitate a fundamental domain, quotient space and universal covering for the quotient. We exhibit this on a non-properly discontinuous free action on ℝ. For a certain class of non-properly discontinuous group actions on the upper half-plane, we use our local data to build a space on which the group acts discretely and cocompactly. Our combinatorial approach to reconstructing abstract group actions on sets is a generalization of the Bass–Serre theory for reconstructing group actions on trees. Our results also provide a generalization of the notion of developable complexes of groups by Haefliger.

The Structure of Semisimple Symmetric Spaces

1979 ◽  
Vol 31 (1) ◽  
pp. 157-180 ◽  
Author(s):  
W. Rossmann
Keyword(s):  
Symmetric Spaces ◽  
Automorphism Groups ◽  
General Structure ◽  
Point Group ◽  
Open Subgroup ◽  
Structure Theory ◽  
Semisimple Lie Groups ◽  
Riemannian Symmetric Spaces

A semisimple symmetric space can be defined as a homogeneous space G/H, where G is a semisimple Lie group, H an open subgroup of the fixed point group of an involutive automorphism of G. These spaces can also be characterized as the affine symmetric spaces or pseudo-Riemannian symmetric spaces or symmetric spaces in the sense of Loos [4] with semisimple automorphism groups [3, 4]. The connected semisimple symmetric spaces are all known: they have been classified by Berger [2] on the basis of Cartan's classification of the Riemannian symmetric spaces. However, the list of these spaces is much too long to make a detailed case by case study feasible. In order to do analysis on semisimple symmetric spaces, for example, one needs a general structure theory, just as in the case of Riemannian symmetric spaces and semisimple Lie groups.

Quantum Field Theories at Small Distances

1961 ◽  
Vol 16 (12) ◽  
pp. 1265-1289
Author(s):  
W. Güttinger ◽  
J. A. Swieca
Keyword(s):  
General Structure ◽  
Form Factors ◽  
Positive Definiteness ◽  
Point Interaction ◽  
Field Theories ◽  
Structure Theory ◽  
Quantum Field Theories ◽  
Matrix Formalism ◽  
Finite Theory ◽  
Limiting Case

The behaviour of the propagation functions of quantized field theories at small distances is investigated in connection with the problem of consistency of the perturbation theoretical renormalization scheme. An attempt is made to adapt the conventional Hamiltonian and S-matrix formalism to the renormalization concept in such a way that a finite theory of interacting physical (dressed) particles results which as a whole and at each step of approximation satisfies the axioms of the general structure theory of quantized fields, notably causality and positive definiteness. If the physical particles of a field theory with point interaction are extended objects owing to the extension of the cloud of virtual quanta in the physical states, then the theory admits of a finite formulation with the extent of the cloud introducing a natural, coupling-dependent built-in cutoff. The limiting case of a pointlike cloud corresponds to physical particles which because of their strong self-interaction do not interact with one another. This case, corresponding to the zero coupling limit, represents the most singular one given by the theory. An increase of interaction or coupling implies an increase of the size of the cloud and a corresponding charge spread. Conversely, there cannot be interaction if there is no extended cloud and charge spread. Cloud and charge structure come in via causal form factors related to vertex parts and electromagnetic form factors, which however a perturbation theoretical scheme cannot take into account.

scholarly journals CLASSROOM COMMUNICATIVE STRUCTURE: EXCHANGE STRUCTURE IN EFL CLASS IN PUBLIC SENIOR HIGH SCHOOL 3 MOJOKERTO

2018 ◽  
Vol 1 (1) ◽  
pp. 9-21
Author(s):  
Reza Fitri Rafsanjani ◽  
Ni Ketut Mirahayuni
Keyword(s):  
High School ◽  
General Structure ◽  
Structure Theory ◽  
Classroom Communication ◽  
Information Giving ◽  
English Class ◽  
Qualitative Descriptive ◽  
Exchange Structure ◽  
Communicative Structure ◽  
Descriptive Method

This article reported the study about classroom communicative structure between teacher and students in English class in Public School High School 3 Mojokerto. This study aims to identify the elements of minimal exchange structure and general exchange structure in communication in classroom. This study uses minimal exchange structure theory of Strenstrom (1994) by qualitative descriptive method. Data in this study are obtained from the recording of conversation among teacher and students of XI grade in Speaking class. The result shows that there are three (3) types  of act as the element of exchange structure:  Initiating, Responding, dan Following-Up (I-R-F). Minimal exchange structure  consists of: Initiating-Responding (I-R) or Initiating-Responding-Following Up (I-R-F). General structure of exchange in classroom situation consists of: greeting, followed by any kinds of functions such as giving information, giving order, and asking question. In conversation, teacher tends to has initiative to start it, meanwhile, the students tend to give respond by doing activity (evade) which are instructed by the teacher. The students sometimes did not answer the question, therefore teacher keeps the conversation going by undergone initiative actions such as giving information, asking question or giving instruction. This study shows that teacher has power to supervise and keep going the class activity.  It is needed to do further study  on power aspect in classroom communication.

scholarly journals Algebraic and Diagonable Rings

1956 ◽  
Vol 8 ◽  
pp. 341-354 ◽  
Author(s):  
M. P. Drazin
Keyword(s):  
General Theory ◽  
General Structure ◽  
Structure Theory ◽  
Precise Information ◽  
Precise Nature ◽  
Definition Of

1. Introduction. In a well-known paper (7) Jacobson has shown how his structure theory for arbitrary rings can be applied to give more precise information about the so-called “algebraic” algebras. This specialization of his general theory is, however, perhaps not completely satisfying in that it deals only with algebras, i.e. rings admitting a field of operators, whereas neither the general structure theory nor the definition of the property of being “algebraic” seems to depend in any essential way on the precise nature of the operators.

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