About the irreflexivity hypothesis for free left distributive magmas

A controllable drift-free system on the Lie group G=SO(3)×R3×R3 is considered. The dynamics and geometrical properties of the corresponding reduced Hamilton’s equations on g∗,·,·- are studied, where ·,·- is the minus Lie-Poisson structure on the dual space g∗ of the Lie algebra g=so(3)×R3×R3 of G. The numerical integration of this system is also discussed.

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Finite submonoids of free left regular bands with unit

Algebra i logika ◽

10.33048/alglog.2020.59.604 ◽

2021 ◽

Vol 59 (6) ◽

pp. 680-701

Author(s):

A. N. Shevlyakov

Keyword(s):

Left Regular ◽

Free Left ◽

Left Regular Bands

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Definability problems for modules and rings

Journal of Symbolic Logic ◽

10.2307/2272466 ◽

1971 ◽

Vol 36 (4) ◽

pp. 623-649 ◽

Cited By ~ 38

Author(s):

Gabriel Sabbagh ◽

Paul Eklof

Keyword(s):

Ring Theory ◽

Noetherian Rings ◽

Fixed Ring ◽

Injective Modules ◽

Free Left ◽

Right Noetherian Rings ◽

The Right

This paper is concerned with questions of the following kind: let L be a language of the form Lαω and let be a class of modules over a fixed ring or a class of rings; is it possible to define in L? We will be mainly interested in the cases where L is Lωω or L∞ω and is a familiar class in homologic algebra or ring theory.In Part I we characterize the rings Λ such that the class of free (respectively projective, respectively flat) left Λ-modules is elementary. In [12] we solved the corresponding problems for injective modules; here we show that the class of injective Λ-modules is definable in L∞ω if and only if it is elementary. Moreover we identify the right noetherian rings Λ such that the class of projective (respectively free) left Λ-modules is definable in L∞ω.

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Noncommutative inclusion–exclusion, representations of left regular bands and the Tsetlin library

International Journal of Algebra and Computation ◽

10.1142/s021819672150003x ◽

2020 ◽

pp. 1-26

Author(s):

Guy Blachar ◽

Louis H. Rowen ◽

Uzi Vishne

Keyword(s):

Regular Band ◽

Left Regular ◽

Free Left ◽

Left Regular Band ◽

The Absolute ◽

Left Regular Bands

We find a semigroup [Formula: see text], whose category of partial representations contains the representation category [Formula: see text] of the free left regular band [Formula: see text]. We use this to construct a resolution for the absolute kernel of a representation of [Formula: see text], for which the kernel [Formula: see text] of the Markov operation in the Tsetlin library model is a prominent example. We obtain a formula for the dimension of the absolute kernel, generalizing the equality of the dimension of [Formula: see text] to the number of derangements of order [Formula: see text].

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Rupture of the Free Left Ventricular Wall: A Novel Approach for Reconstruction

The Thoracic and Cardiovascular Surgeon Reports ◽

10.1055/s-0038-1642613 ◽

2018 ◽

Vol 07 (01) ◽

pp. e30-e32

Author(s):

Felix Fleißner ◽

Jan Schmitto ◽

L. Christian Napp ◽

Issam Ismail

Keyword(s):

Left Ventricular ◽

Left Ventricular Wall ◽

Reconstruction Method ◽

Ventricular Wall ◽

Free Wall ◽

Urgent Surgery ◽

Emergent Operation ◽

Novel Approach ◽

Free Left ◽

Free Left Ventricular Wall

Background A rupture of the free wall of the left ventricle is a rarely seen complication of myocardial infarction and represents an absolute cardiac emergency. Case Description We hereby present a case of a 64-year-old patient with a rupture of the free left ventricular wall. The patient was treated in an emergent operation with a novel reconstruction method of the left ventricular wall and was discharged 30 days after the initial operation. Conclusion Left ventricular free wall rupture is rarely described in the literature, which might be because of high mortality in underdiagnosed cases. Therefore, early imaging by echo or computed tomography (CT) is essential for detecting this dangerous condition. Once diagnosed, urgent surgery is mandatory to save the life of the patient.

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The activation of the free left ventricular wall in the dog's heart

American Heart Journal ◽

10.1016/0002-8703(55)90077-6 ◽

1955 ◽

Vol 49 (4) ◽

pp. 587-602 ◽

Cited By ~ 48

Author(s):

Demetrio Sodi-Pallares ◽

Abdo Bisteni ◽

Gustavo A. Medrano ◽

Fernando Cisneros

Keyword(s):

Left Ventricular ◽

Left Ventricular Wall ◽

Ventricular Wall ◽

Free Left ◽

Free Left Ventricular Wall

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Abelian varieties isogenous to a power of an elliptic curve

Compositio Mathematica ◽

10.1112/s0010437x17007990 ◽

2018 ◽

Vol 154 (5) ◽

pp. 934-959 ◽

Cited By ~ 2

Author(s):

Bruce W. Jordan ◽

Allan G. Keeton ◽

Bjorn Poonen ◽

Eric M. Rains ◽

Nicholas Shepherd-Barron ◽

...

Keyword(s):

Elliptic Curve ◽

Abelian Variety ◽

Opposite Direction ◽

Abelian Varieties ◽

Sufficient Conditions ◽

Higher Dimensional ◽

Free Left ◽

Necessary And Sufficient ◽

Finitely Presented ◽

Torsion Free

Let $E$ be an elliptic curve over a field $k$. Let $R:=\operatorname{End}E$. There is a functor $\mathscr{H}\!\mathit{om}_{R}(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a power of $E$, and a functor $\operatorname{Hom}(-,E)$ in the opposite direction. We prove necessary and sufficient conditions on $E$ for these functors to be equivalences of categories. We also prove a partial generalization in which $E$ is replaced by a suitable higher-dimensional abelian variety over $\mathbb{F}_{p}$.

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