Artin's problem for skew field extensions

1985 ◽  
Vol 97 (1) ◽  
pp. 1-6 ◽  
Author(s):  
A. H. Schofield
Keyword(s):  
Artinian Ring ◽  
Field Extension ◽  
Subsequent Paper ◽  
Commutative Field ◽  
Finite Representation ◽  
New Approach ◽  
Skew Field ◽  
Skew Fields ◽  
Left And Right ◽  
The Right

For a commutative field extension, L ⊃ K, it is clear that a left basis of L over K; is also a right basis of L over K; however, for an extension of skew fields, this may easily fail, though it is hard to determine whether the right and left dimension may be different. Cohn ([4], ch. 5), however, was able to find extensions of skew fields such that the left and right dimensions were an arbitrary pair of cardinals subject only to the restrictions that neither were 1 and at least one of them was infinite. In this paper, I shall present a new approach that allows us to construct extensions of skew fields such that the left and right dimensions are arbitrary integers not equal to 1. In a subsequent paper, [7], I shall present related results and consequences; in particular, there is a construction of a hereditary artinian ring of finite representation type corresponding to the Coxeter diagram I2(5) answering the question raised by Dowbor, Ringel and Simson[5].

Hereditary artinian rings of finite representation type and extensions of simple artinian rings

1987 ◽  
Vol 102 (3) ◽  
pp. 411-420 ◽  
Author(s):  
Aidan Schofield
Keyword(s):  
Artinian Ring ◽  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Artinian Rings ◽  
Finite Dimensional ◽  
Coxeter Diagram ◽  
Skew Fields ◽  
Left And Right ◽  
Natural Way

In [1], Dowbor, Ringel and Simson consider hereditary artinian rings of finite representation type; it is known that if A is an hereditary artinian algebra of finite representation type, finite-dimensional over a field, then it corresponds to a Dynkin diagram in a natural way; they show that an hereditary artinian ring of finite representation type corresponds to a Coxeter diagram. However, in order to construct an hereditary artinian ring of finite representation type corresponding to a Coxeter diagram that is not Dynkin, they show that it is necessary though not sufficient to find an extension of skew fields such that the left and right dimensions are both finite but are different. No examples of such skew fields were known at the time. In [3], I constructed such extensions, and the main aim of this paper is to extend the methods of that paper to construct an extension of skew fields having all the properties needed to construct an hereditary artinian ring of finite representation type corresponding to the Coxeter diagram I2(5).

The word problem for free fields

1973 ◽  
Vol 38 (2) ◽  
pp. 309-314 ◽  
Author(s):  
P. M. Cohn
Keyword(s):  
Normal Form ◽  
Word Problem ◽  
Free Field ◽  
Free Associative Algebra ◽  
Commutative Field ◽  
Skew Field ◽  
Solvable Word Problem ◽  
Skew Fields ◽  
Free Fields ◽  
Solvable Word

It has long been known that every free associative algebra can be embedded in a skew field [11]; in fact there are many different embeddings, all obtainable by specialization from the ‘universal field of fractions’ of the free algebra (cf. [5, Chapter 7]). This makes it reasonable to call the latter the free field; see §2 for precise definitions. The existence of this free field was first established by Amitsur [1], but his proof is rather indirect and does not provide anything like a normal form for the elements of the field. Actually one cannot expect to find such a normal form, since it does not even exist in the field of fractions of a commutative integral domain, but at least one can raise the word problem for free fields: Does there exist an algorithm for deciding whether a given expression for an element of the free field represents zero?Now some recent work has revealed a more direct way of constructing free fields ([4], [5], [6]), and it is the object of this note to show how this method can be used to solve the word problem for free fields over infinite ground fields. In this connexion it is of interest to note that A. Macintyre [9] has shown that the word problem for skew fields is recursively unsolvable. Of course, every finitely generated commutative field has a solvable word problem (see e.g. [12]).The construction of universal fields of fractions in terms of full matrices is briefly recalled in §2, and it is shown quite generally for a ring R with a field of fractions inverting all full matrices, that if the set of full matrices over R is recursive, then the universal field has a solvable word problem. This holds more generally if the precise set of matrices over R inverted over the field is recursive, but it seems difficult to exploit this more general statement.

When the State Speaks, What Should It Say?

2012 ◽  
Author(s):  
Corey Brettschneider
Keyword(s):  
Freedom Of Expression ◽  
The State ◽  
Hate Groups ◽  
New Approach ◽  
State Action ◽  
Democratic State ◽  
Theory Of Value ◽  
The Right ◽  
Equal Citizenship ◽  
The Ideal

How should a liberal democracy respond to hate groups and others that oppose the ideal of free and equal citizenship? The democratic state faces the hard choice of either protecting the rights of hate groups and allowing their views to spread, or banning their views and violating citizens' rights to freedoms of expression, association, and religion. Avoiding the familiar yet problematic responses to these issues, this book proposes a new approach called value democracy. The theory of value democracy argues that the state should protect the right to express illiberal beliefs, but the state should also engage in democratic persuasion when it speaks through its various expressive capacities: publicly criticizing, and giving reasons to reject, hate-based or other discriminatory viewpoints. Distinguishing between two kinds of state action—expressive and coercive—the book contends that public criticism of viewpoints advocating discrimination based on race, gender, or sexual orientation should be pursued through the state's expressive capacities as speaker, educator, and spender. When the state uses its expressive capacities to promote the values of free and equal citizenship, it engages in democratic persuasion. By using democratic persuasion, the state can both respect rights and counter hateful or discriminatory viewpoints. The book extends this analysis from freedom of expression to the freedoms of religion and association, and shows that value democracy can uphold the protection of these freedoms while promoting equality for all citizens.

Comparison of the efficiency of the indexes of Pont and Korkhause with Kernott technique in patients with narrowing of maxilla

2020 ◽  
Vol 20 (3) ◽  
pp. 199-203
Author(s):  
O. I. Admakin ◽  
I. A. Solop ◽  
A. D. Oksentyuk
Keyword(s):  
Dental Treatment ◽  
Standard Analysis ◽  
Clinical Hospital ◽  
Control Models ◽  
Diagnostic Models ◽  
Left And Right ◽  
The Asymmetry ◽  
The Right ◽  
The University ◽  
Medical University

Relevance. The narrowing of the maxilla is one of the most common pathologies in orthodontics. Recent studies show that the narrowing is always asymmetric which is connected to the rotation of the maxilla. To choose the treatment correctly one need a calculation that reveals the asymmetry, which is impossible with using standard indexes.Purpose – to compare efficiency of indexes of Pont and Korkhause with the Kernott's method in patients with narrowing of the maxilla.Materials and methods. The study involved 35 children aged from 8 to 12 years old undergoing dental treatment in the University Children's Clinical Hospital of the First Moscow State Medical University with no comorbidities. For every patient a gypsum model was prepared and after that to carry out the biometrical calculation. In this study two indexes were used: Pont's index and Korkhause's; using this standard analysis the narrowing of the maxilla was revealed. After using Pont's Index and Korkhaus analysis all the models were calculated by the method of Kernott with Kernott's dynamic pentagon.Results. As a result of the analysis of the control diagnostic models a narrowing of the maxilla in 69% of cases (n = 24) was revealed in all cases, the deviation of the size of the dentition was asymmetric. Thus, 65% of the surveyed models showed a narrowing on the right. This narrowing was of a different severity and averaged 15 control models.Conclusions. This shows that for the biometrics of diagnostic models it is necessary to use methods that allow to estimate the width of the dentition rows on the left and on the right separately. To correct the asymmetric narrowing of the dentition, it is preferable to use non-classical expanding devices that act equally on the left and right sides separetly.

scholarly journals Transcriptomic uniqueness and commonality of the ion channels and transporters in the four heart chambers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sanda Iacobas ◽  
Bogdan Amuzescu ◽  
Dumitru A. Iacobas
Keyword(s):  
Ion Channels ◽  
Cycle Phase ◽  
Functional Roles ◽  
Expression Control ◽  
Gene Expression Control ◽  
Left And Right ◽  
The Right ◽  
Phase Out ◽  
Right Atria ◽  
Agilent Microarrays

AbstractMyocardium transcriptomes of left and right atria and ventricles from four adult male C57Bl/6j mice were profiled with Agilent microarrays to identify the differences responsible for the distinct functional roles of the four heart chambers. Female mice were not investigated owing to their transcriptome dependence on the estrous cycle phase. Out of the quantified 16,886 unigenes, 15.76% on the left side and 16.5% on the right side exhibited differential expression between the atrium and the ventricle, while 5.8% of genes were differently expressed between the two atria and only 1.2% between the two ventricles. The study revealed also chamber differences in gene expression control and coordination. We analyzed ion channels and transporters, and genes within the cardiac muscle contraction, oxidative phosphorylation, glycolysis/gluconeogenesis, calcium and adrenergic signaling pathways. Interestingly, while expression of Ank2 oscillates in phase with all 27 quantified binding partners in the left ventricle, the percentage of in-phase oscillating partners of Ank2 is 15% and 37% in the left and right atria and 74% in the right ventricle. The analysis indicated high interventricular synchrony of the ion channels expressions and the substantially lower synchrony between the two atria and between the atrium and the ventricle from the same side.

The role of visual experience for spatial numerical associations

2012 ◽  
Vol 25 (0) ◽  
pp. 222 ◽  
Author(s):  
Michael J. Proulx ◽  
Achille Pasqualotto ◽  
Shuichiro Taya
Keyword(s):  
Visual Experience ◽  
Opposite Effect ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Generation Task ◽  
Congenitally Blind ◽  
Left And Right ◽  
The Right

The topographic representation of space interacts with the mental representation of number. Evidence for such number–space relations have been reported in both synaesthetic and non-synaesthetic participants. Thus far most studies have only examined related effects in sighted participants. For example, the mental number line increases in magnitude from left to right in sighted individuals (Loetscher et al., 2008, Curr. Biol.). What is unclear is whether this association arises from innate mechanisms or requires visual experience early in life to develop in this way. Here we investigated the role of visual experience for the left to right spatial numerical association using a random number generation task in congenitally blind, late blind, and blindfolded sighted participants. Participants orally generated numbers randomly whilst turning their head to the left and right. Sighted participants generated smaller numbers when they turned their head to the left than to the right, consistent with past results. In contrast, congenitally blind participants generated smaller numbers when they turned their head to the right than to the left, exhibiting the opposite effect. The results of the late blind participants showed an intermediate profile between that of the sighted and congenitally blind participants. Visual experience early in life is therefore necessary for the development of the spatial numerical association of the mental number line.

scholarly journals Surface Evolution During Semiconductor Processing

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 379-384 ◽  
Author(s):  
Ganesh Rajagopalan ◽  
Vadali Mahadev ◽  
Timothy S. Cale
Keyword(s):  
Riemann Problem ◽  
Surface Profile ◽  
Numerical Implementation ◽  
Jump Conditions ◽  
Semiconductor Processing ◽  
Explicit Integration ◽  
Surface Evolution ◽  
Left And Right ◽  
The Right ◽  
Surface Angle

We discuss our approach to using the Riemann problem to compute surface profile evolution during the simulation of deposition, etch and reflow processes. Each pair of segments which represents the surface is processed sequentially. For cases in which both segments are the same material, the Riemann problem is solved. For cases in which the two segments are different materials, two Riemann problems are solved. The material boundary is treated as the right segment for the left material and as the left segment for the right material. The critical equations for the analyses are the characteristics of the Riemann problem and the ‘jump conditions’ which represent continuity of the surface. Examples are presented to demonstrate selected situations. One limitation of the approach is that the velocity of the surface is not known as a function of the surface angle. Rather, it is known for the angles of the left and right segments. The rate as a function of angle must be assumed for the explicit integration procedure used. Numerical implementation is briefly discussed.

scholarly journals Ventilation/perfusion mismatch during lung aeration at birth

2014 ◽  
Vol 117 (5) ◽  
pp. 535-543 ◽  
Author(s):  
Justin A. R. Lang ◽  
James T. Pearson ◽  
Arjan B. te Pas ◽  
Megan J. Wallace ◽  
Melissa L. Siew ◽  
...  
Keyword(s):  
Pulmonary Arteries ◽  
Left Lung ◽  
X Ray ◽  
Lung Aeration ◽  
X Ray Imaging ◽  
Iodine Level ◽  
Pulmonary Shunting ◽  
Left And Right ◽  
Near Term ◽  
The Right

At birth, the transition to newborn life is triggered by lung aeration, which stimulates a large increase in pulmonary blood flow (PBF). Current theories predict that the increase in PBF is spatially related to ventilated lung regions as they aerate after birth. Using simultaneous phase-contrast X-ray imaging and angiography we investigated the spatial relationships between lung aeration and the increase in PBF after birth. Six near-term (30-day gestation) rabbits were delivered by caesarean section, intubated and an intravenous catheter inserted, before they were positioned for X-ray imaging. During imaging, iodine was injected before ventilation onset, after ventilation of the right lung only, and after ventilation of both lungs. Unilateral ventilation increased iodine levels entering both left and right pulmonary arteries (PAs) and significantly increased heart rate, iodine ejection per beat, diameters of both left and right PAs, and number of visible vessels in both lungs. Within the 6th intercostal space, the mean gray level (relative measure of iodine level) increased from 68.3 ± 11.6 and 70.3 ± 7.5%·s to 136.3 ± 22.6 and 136.3 ± 23.7%·s in the left and right PAs, respectively. No differences were observed between vessels in the left and right lungs, despite the left lung not initially being ventilated. The increase in PBF at birth is not spatially related to lung aeration allowing a large ventilation/perfusion mismatch, or pulmonary shunting, to occur in the partially aerated lung at birth.

Handedness affects Emotional Valence Asymmetry

1989 ◽  
Vol 68 (2) ◽  
pp. 435-441 ◽  
Author(s):  
Richard A. McFarland ◽  
Robert Kennison
Keyword(s):  
Negative Affect ◽  
Hemispheric Asymmetry ◽  
Emotional Responses ◽  
Emotional Valence ◽  
Left Handed ◽  
Two Factors ◽  
Left And Right ◽  
The Asymmetry ◽  
The Right ◽  
Cerebral Processing

Music was played monaurally to 80 right-handed and 80 left-handed subjects. Right-handers reported more positive and less negative affect if the music was to the right ear. Left-handers reported experiencing more positive and less negative affect during music to the left ear. The hand × ear interaction was significant. The valence of emotional responses to the music seems influenced by a combination of at least two factors, (1) differences between left- and right-handers in the cerebral processing of emotional valence and (2) differences in the processing of emotional valence within each handedness group depending upon which hemisphere was initially most strongly engaged by the music. These results partially corroborate and extend the findings of previous studies in which briefer stimuli were presented tachistoscopically or dichotically. It is concluded that, while there is hemispheric asymmetry in the processing of emotional valence, the direction of the asymmetry may be associated with the handedness of the subjects.

THE METHOD FOR EVALUATING ADAPTIVE CHANGES IN HUMAN MICROCIRCULATORY-TISSUE SYSTEMS

2020 ◽  
Vol 4 (1) ◽  
pp. 88-99
Author(s):  
A.V. DUNAEV
Keyword(s):  
Middle Finger ◽  
Analysis Data ◽  
The Body ◽  
Tissue Oxygen Saturation ◽  
Doppler Flowmetry ◽  
New Approach ◽  
Adaptive Changes ◽  
Palmar Surface ◽  
Tissue Systems ◽  
The Right

The work is aimed at developing a new approach to assessing adaptive changes in microcirculatory tissue systems when various loads are exerted on the body (sports or physiological stresses), based on the analysis of oscillations in microcirculatory blood flow and tissue oxygen saturation, measured by laser Doppler flowmetry (LDF) and tissue reflectance oximetry (TRO). The study involved eight healthy volunteers aged 21–49 years. Measurements were taken on the palmar surface of the middle finger of the right hand and the medial surface of the lower part of the forearm. The rhythmic oscillations of LDF and TRO were studied using wavelet analysis. Data analysis revealed resonant and synchronized oscillations in the LDF and TRO signals in the myogenic range as an adaptive change as a result of a reaction to physical activity and psychoemotional stress.

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