A lattice of extension rings for a commutative ring

1978 ◽  
Vol 84 (2) ◽  
pp. 225-234 ◽  
Author(s):  
D. Kirby ◽  
M. R. Adranghi
Keyword(s):  
Point Of View ◽  
Local Rings ◽  
Algebraic Point ◽  
Multiple Points ◽  
One Dimensional ◽  
Maximal Ideals ◽  
Blowing Up ◽  
Abstract Case ◽  
Algebroid Curve

The work of this note was motivated in the first place by North-cott's theory of dilatations for one-dimensional local rings (see, for example (4) and (5)). This produces a tree of local rings as in (4) which corresponds, in the abstract case, to the branching sequence of infinitely-near multiple points on an algebroid curve. From the algebraic point of view it seems more natural to characterize such one-dimensional local rings R by means of the set of rings which arise by blowing up all ideals Q which are primary for the maximal ideals M of R. This set of rings forms a lattice (R), ordered by inclusion, each ring S of which is a finite R-module. Moreover the length of the R-module S/R is just the reduction number of the corresponding ideal Q (cf. theorem 1 of Northcott (6)). Thus the lattice (R) provides a finer classification of the rings R than does the set of reduction numbers (cf. Kirby (1)).

Workspace Analysis of Multibody Mechanical Systems Using Continuation Methods

1988 ◽  
Author(s):  
D.-Y. Jo ◽  
E. J. Haug
Keyword(s):  
Mechanical Systems ◽  
Point Of View ◽  
Continuation Methods ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Generalized Coordinates ◽  
Workspace Analysis ◽  
Manifold Mapping ◽  
Manifold Theory

Abstract A new approach to numerical analysis of workspaces of multibody mechanical systems is developed. Numerical techniques that are based on manifold theory and utilize continuation methods are presented and applied to a variety of mechanical systems, including closed-loop mechanisms. Generalized coordinates that define kinematics of a system are classified and interpreted from an input-output point of view. Boundaries of workspaces, which depend on the classification of generalized coordinates, are defined as sets of singular points of Jacobians of the kinematic equations. Numerical methods for tracing one dimensional trajectories on a workspace boundary are outlined and example are analyzed using one dimensional manifold mapping computer programs, such as PITCON and AUTO.

scholarly journals WHERE ARE ELKO SPINOR FIELDS IN LOUNESTO SPINOR FIELD CLASSIFICATION?

2006 ◽  
Vol 21 (01) ◽  
pp. 65-74 ◽  
Author(s):  
R. DA ROCHA ◽  
W. A. RODRIGUES
Keyword(s):  
Spinor Field ◽  
Point Of View ◽  
Algebraic Point ◽  
General Classification ◽  
Spinor Fields ◽  
Majorana Spinor ◽  
Algebraic Constraints ◽  
Elko Spinor Fields ◽  
Component Spinor

This paper proves that from the algebraic point of view ELKO spinor fields belong together with Majorana spinor fields to a wider class, the so-called flagpole spinor fields, corresponding to the class 5, according to Lounesto spinor field classification. We show moreover that algebraic constraints imply that any class 5 spinor field is such that the 2-component spinor fields entering its structure have opposite helicities. The proof of our statement is based on Lounesto general classification of all spinor fields, according to the relations and values taken by their associated bilinear covariants, and can eventually shed some new light on the algebraic investigations concerning dark matter.

scholarly journals Distilling Entanglement from Fermions

2009 ◽  
Vol 16 (02n03) ◽  
pp. 243-258
Author(s):  
Michael Keyl
Keyword(s):  
Hilbert Spaces ◽  
Point Of View ◽  
Entangled States ◽  
Algebraic Point ◽  
Gaussian States ◽  
Free Fermions ◽  
One Dimensional ◽  
Fermionic Systems ◽  
Maximally Entangled States ◽  
Local Observables

Since fermions are based on anti-commutation relations, their entanglement cannot be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of separable and of maximally entangled states. In this paper we want to discuss local operations and entanglement distillation from bipartite fermionic systems. To this end we apply an algebraic point of view where algebras of local observables, rather than tensor product Hilbert spaces play the central role. We apply our scheme in particular to fermionic Gaussian states, where the whole discussion can be reduced to properties of the covariance matrix. Finally, the results are demonstrated with free fermions on an infinite, one-dimensional lattice.

scholarly journals A General Theory of One-dimensional Local Rings

1956 ◽  
Vol 2 (4) ◽  
pp. 159-169 ◽  
Author(s):  
D. G. Northcott
Keyword(s):  
Residue Field ◽  
Integral Closure ◽  
Point Of View ◽  
Local Rings ◽  
Abstract Theory ◽  
Special Situation ◽  
Quotient Field ◽  
Geometric Problem ◽  
One Dimensional ◽  
General Abstract

The development of the theory of local rings has been greatly stimulated by the importance of the applications to algebraic geometry, but it is none the less true that this stimulus has produced a theory which, on aesthetic grounds, is somewhat unsatisfactory. In the first place, if a local ring Q arises in the ordinary way from a geometric problem, then Qwill have the same characteristic as its residue field. It is partly for this reason that our knowledge of equicharacteristic local rings is much more extensive than it is of those local rings which present the case of unequal characteristics. Again, in the geometric case, the integral closure of Q in its quotient field will be a finite Q-module. Here, once more, we have a special situation which it would be desirable to abandon from the point of view of a general abstract theory.

scholarly journals On the Canonical Ideals of One-Dimensional Cohen–Macaulay Local Rings

2015 ◽  
Vol 59 (1) ◽  
pp. 77-90 ◽  
Author(s):  
Juan Elias
Keyword(s):  
High Power ◽  
Maximal Ideal ◽  
Local Rings ◽  
Gorenstein Rings ◽  
One Dimensional ◽  
Analytic Classification ◽  
Curve Singularities

AbstractIn this paper we consider the problem of explicitly finding canonical ideals of one-dimensional Cohen–Macaulay local rings. We show that Gorenstein ideals contained in a high power of the maximal ideal are canonical ideals. In the codimension 2 case, from a Hilbert–Burch resolution, we show how to construct canonical ideals of curve singularities. Finally, we translate the problem of the analytic classification of curve singularities to the classification of local Artin Gorenstein rings with suitable length.

scholarly journals The combinatorics of an algebraic class of easy quantum groups

2014 ◽  
Vol 17 (03) ◽  
pp. 1450016 ◽  
Author(s):  
Sven Raum ◽  
Moritz Weber
Keyword(s):  
Symmetric Group ◽  
Quantum Group ◽  
Permutation Group ◽  
Free Product ◽  
Quantum Groups ◽  
Orthogonal Group ◽  
Point Of View ◽  
Algebraic Point ◽  
Matrix Quantum

Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group Sn and the orthogonal group On as well as Wang's quantum permutation group [Formula: see text] and his free orthogonal quantum group [Formula: see text]. In this paper, we study a particular class of categories of partitions to each of which we assign a subgroup of the infinite free product of the cyclic group of order two. This is an important step in the classification of all easy quantum groups and we deduce that there are uncountably many of them. We focus on the combinatorial aspects of this assignment, complementing the quantum algebraic point of view presented in another paper.

scholarly journals On the classification of the Lie algebrasLr,ts

2004 ◽  
Vol 2004 (42) ◽  
pp. 2269-2272
Author(s):  
L. A-M. Hanna
Keyword(s):  
Lie Algebras ◽  
Isomorphism Class ◽  
Matrix Representation ◽  
Point Of View ◽  
Algebraic Point

The Lie algebrasLr,tsintroduced by the author (2003) are classified from an algebraic point of view. A matrix representation of least degree is given for each isomorphism class.

RHYNCHOLITES AND THE PROBLEM OF NARROW AND BROAD CONCEPTION OF TAXONS

2018 ◽  
pp. 12-17 ◽  
Author(s):  
I. R. Khuzina ◽  
V. N. Komarov
Keyword(s):  
Sexual Dimorphism ◽  
Morphological Characteristics ◽  
Mass Scale ◽  
Individual Variability ◽  
Point Of View ◽  
The Other ◽  
New Taxon ◽  
Artificial System ◽  
Broad Understanding

The paper considers a point of view, based on the conception of the broad understanding of taxons. According to this point of view, rhyncholites of the subgenus Dentatobeccus and Microbeccus are accepted to be synonymous with the genus Rhynchoteuthis, and subgenus Romanovichella is considered to be synonymous with the genus Palaeoteuthis. The criteria, exercising influence on the different approaches to the classification of rhyncholites, have been analyzed (such as age and individual variability, sexual dimorphism, pathological and teratological features, degree of disintegration of material), underestimation of which can lead to inaccuracy. Divestment of the subgenuses Dentatobeccus, Microbeccus and Romanovichella, possessing very bright morphological characteristics, to have an independent status and denomination to their synonyms, has been noted to be unjustified. An artificial system (any suggested variant) with all its minuses is a single probable system for rhyncholites. The main criteria, minimizing its negative sides and proving the separation of the new taxon, is an available mass-scale material. The narrow understanding of the genus, used in sensible limits, has been underlined to simplify the problem of the passing the view about the genus to the other investigators and recognition of rhyncholites for the practical tasks.

LEGAL, MORAL AND ETHICAL SIDE OF THE OFFENSE, DISCREDITING HONOR EMPLOYEE THE PENAL SYSTEM

2020 ◽  
Vol 10 (2) ◽  
pp. 213-218
Author(s):  
OKSANA KOCHKINA ◽  
◽  
OLGA MARCHUK ◽  
Keyword(s):  
Point Of View ◽  
Professional Activity ◽  
Penal System ◽  
Moral Norms ◽  
Ethical Aspects ◽  
Self Assessment ◽  
Personal Qualities ◽  
Executive System ◽  
Correction System

The article examines the legal and moral and ethical aspects of a misdemeanor that discredits the honor of an employee of the criminal Executive system. The considered reason for dismissal has the main feature associated with the integration of legal and moral norms, which often raises a lot of questions about the attribution of a particular offense to this basis. Using the analysis of normative legal acts, the authors attempt to identify the signs that contribute to the separation of the studied grounds for dismissal from all their diversity. The classification of offenses that discredit the honor of an employee of the criminal Executive system is presented, which allows to systematize and organize the knowledge obtained about the considered grounds for dismissal. The analysis of a misdemeanor that defames the honor of an employee of the penal system from a moral and ethical position gives an understanding, first of all, that it does not have a clear regulation from the point of view of the law, but the consequences of committing such a misdemeanor are clearly legal. The concepts of “honor” and “dignity” are considered as ethical categories and are analyzed as personal qualities that are manifested in an employee of the penal correction system during the period of service. These categories in the behavior of a person or employee are manifested both externally (assessment from the outside) and internally (self-assessment). The article describes the value orientation of an employee of the criminal Executive system to ethical standards in professional activity, which is an integral part of the moral and ethical side of a misdemeanor that discredits the honor of an employee.

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