COMPOSITION SERIES OF THE SOLVABLE ABELIAN FACTOR GROUP SOURCE OF EQUATION OF ALL POLYNOMIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 462-469
Author(s):  
Bernard Alechenu ◽  
Babayo Muhammed Abdullahi ◽  
Daniel Eneojo Emmanuel
Keyword(s):  
Abelian Group ◽  
Complex Analysis ◽  
Factor Group ◽  
Roots Of Unity ◽  
Composition Series ◽  
Isomorphism Theorem ◽  
Polynomial Equations ◽  
Canonical Map ◽  
The Third ◽  
Recursive Set

This work penciled down the Composition Series of Factor Abelian Group over the source of all polynomial equations gleaned through  the nth roots of unity regular gons on a unit circle, a circle of radius one and centered at zero. To get the composition series, the third isomorphism theorem has to be passed through. But, the third isomorphism theorem itself gleaned via the first which is a deduction of the naturally existing canonical map. The solution of the source atom of the equation of all equation of polynomials are solvable by the intertwine of the Euler’s Formula and the De Moivre’s Theorem which after the inter-math, they become within the domain of complex analysis. For the source root of the equations, there is a recursive set of homomorphisms and ontoness of the mappings geneting the sequential terms in the composition series.    

scholarly journals PENGAMBILAN KEPUTUSAN HUTANG PADA USAHA KECIL DAN MENENGAH (UKM) DI PULAU LOMBOK: SUATU PERSPEKTIF BEHAVIORAL FINANCE

2018 ◽  
Vol 7 (4) ◽  
Author(s):  
Siti Aisyah Hidayati ◽  
Embun Suryani ◽  
M Muhdin
Keyword(s):  
Decision Making ◽  
Behavioral Finance ◽  
Loss Aversion ◽  
Sampling Method ◽  
Confirmation Bias ◽  
Sampling Technique ◽  
Factor Group ◽  
Dominant Factor ◽  
The Third ◽  
Lombok Island

The purpose of this study is to find out what factors determine decision making of debt and what are the most dominant factors in  decision making of debt for SMEs on the island of Lombok.  This research is an explanatory research with quantitative approach. The population is all SMEs located in Lombok island. The sample is selected by Non probability sampling technique with a judgment sampling method where the SMEs that selected as samples are SMEs in handicraft industry of pottery and already exporting the products. Of the existing population, there are 25 (twenty five) SMEs that can be sampled. Respondents in this study are managers who also the owner of the SMEs. Data was collected using questionnaire. To achieve the research objectives, the data obtained will be processed according to needs using Factor Analysis.The results of this study indicate there are three groups of factors that determine  decision making of debt, namely the First Factor Group consists of: Variable Excessive Optimism, Variable Overconfidence, Variable Confirmation Bias and Variable Aversion to sure loss. This factor is named Factor Overconfidence. The Second Factor Group consisted of Representativeness Variables, Avaibility Variables and Anchoring and Adjustment Variables. This factor is named the Avaibility Factor. The third factor group consists of Affect Variables and Aversion Loss Variables. This factor is named the Factor of Loss Aversion. The most dominant factor in determining debt decision making for SMEs in Lombok Island is the Overconfidence factor group consisting of Variable Excessive Optimism, Variable Overconfidence, Variable Confirmation Bias and Variable Aversion to sure loss .

scholarly journals On the classification of Schreier extensions of monoids with non-abelian kernel

2020 ◽  
Vol 32 (3) ◽  
pp. 607-623
Author(s):  
Nelson Martins-Ferreira ◽  
Andrea Montoli ◽  
Alex Patchkoria ◽  
Manuela Sobral
Keyword(s):  
Abelian Group ◽  
Cohomology Group ◽  
Isomorphism Classes ◽  
The Third ◽  
Abelian Kernel ◽  
Invertible Elements ◽  
Abstract Kernel

AbstractWe show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel {\Phi\colon M\to\frac{\operatorname{End}(A)}{\operatorname{Inn}(A)}}. If an abstract kernel factors through {\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}}, where {\operatorname{SEnd}(A)} is the monoid of surjective endomorphisms of A, then we associate to it an obstruction, which is an element of the third cohomology group of M with coefficients in the abelian group {U(Z(A))} of invertible elements of the center {Z(A)} of A, on which M acts via Φ. An abstract kernel {\Phi\colon M\to\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}} (resp. {\Phi\colon M\to\frac{\operatorname{Aut}(A)}{\operatorname{Inn}(A)}}) is induced by a regular weakly homogeneous (resp. homogeneous) Schreier extension of M by A if and only if its obstruction is zero. We also show that the set of isomorphism classes of regular weakly homogeneous (resp. homogeneous) Schreier extensions inducing a given abstract kernel {\Phi\colon M\to\frac{\operatorname{SEnd}(A)}{\operatorname{Inn}(A)}} (resp. {\Phi\colon M\to\frac{\operatorname{Aut}(A)}{\operatorname{Inn}(A)}}), when it is not empty, is in bijection with the second cohomology group of M with coefficients in {U(Z(A))}.

scholarly journals Roots of Elliptic Scator Numbers

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 321
Author(s):  
Manuel Fernandez-Guasti
Keyword(s):  
Abelian Group ◽  
Geometric Interpretation ◽  
Roots Of Unity ◽  
Complex Roots ◽  
De Moivre’S Formula

The Victoria equation, a generalization of De Moivre’s formula in 1+n dimensional scator algebra, is inverted to obtain the roots of a scator. For the qth root in S1+n of a real or a scator number, there are qn possible roots. For n=1, the usual q complex roots are obtained with their concomitant cyclotomic geometric interpretation. For n≥2, in addition to the previous roots, new families arise. These roots are grouped according to two criteria: sets satisfying Abelian group properties under multiplication and sets catalogued according to director conjugation. The geometric interpretation is illustrated with the roots of unity in S1+2.

scholarly journals PENGAMBILAN KEPUTUSAN HUTANG PADA USAHA KECIL DAN MENENGAH (UKM) DI PULAU LOMBOK: SUATU PERSPEKTIF BEHAVIORAL FINANCE

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Siti Aisyah Hidayati ◽  
Embun Suryani ◽  
M Muhdin
Keyword(s):  
Decision Making ◽  
Behavioral Finance ◽  
Loss Aversion ◽  
Sampling Method ◽  
Confirmation Bias ◽  
Sampling Technique ◽  
Factor Group ◽  
Dominant Factor ◽  
The Third ◽  
Lombok Island

The purpose of this study is to find out what factors determine decision making of debt and what are the most dominant factors in  decision making of debt for SMEs on the island of Lombok.  This research is an explanatory research with quantitative approach. The population is all SMEs located in Lombok island. The sample is selected by Non probability sampling technique with a judgment sampling method where the SMEs that selected as samples are SMEs in handicraft industry of pottery and already exporting the products. Of the existing population, there are 25 (twenty five) SMEs that can be sampled. Respondents in this study are managers who also the owner of the SMEs. Data was collected using questionnaire. To achieve the research objectives, the data obtained will be processed according to needs using Factor Analysis.The results of this study indicate there are three groups of factors that determine  decision making of debt, namely the First Factor Group consists of: Variable Excessive Optimism, Variable Overconfidence, Variable Confirmation Bias and Variable Aversion to sure loss. This factor is named Factor Overconfidence. The Second Factor Group consisted of Representativeness Variables, Avaibility Variables and Anchoring and Adjustment Variables. This factor is named the Avaibility Factor. The third factor group consists of Affect Variables and Aversion Loss Variables. This factor is named the Factor of Loss Aversion. The most dominant factor in determining debt decision making for SMEs in Lombok Island is the Overconfidence factor group consisting of Variable Excessive Optimism, Variable Overconfidence, Variable Confirmation Bias and Variable Aversion to sure loss .Keyword:Behavioral finance, decision making of debt, SMEs

scholarly journals On the Koszul map of Lie algebras

2016 ◽  
Vol 28 (1) ◽  
Author(s):  
Yves Cornulier
Keyword(s):  
Abelian Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Free Abelian Group ◽  
Bilinear Maps ◽  
Nilpotent Lie Algebra ◽  
Torsion Free Abelian Group ◽  
The Third ◽  
Torsion Free

AbstractWe motivate and study the reduced Koszul map, relating the invariant bilinear maps on a Lie algebra and the third homology. We show that it is concentrated in degree 0 for any grading in a torsion-free abelian group, and in particular it vanishes whenever the Lie algebra admits a positive grading. We also provide an example of a 12-dimensional nilpotent Lie algebra whose reduced Koszul map does not vanish. In an appendix, we reinterpret the results of Neeb and Wagemann about the second homology of current Lie algebras, which are closely related to the reduced Koszul map.

scholarly journals On the composition series of principal series representations of a three-fold covering group of SL(2, K)

1980 ◽  
Vol 77 ◽  
pp. 177-196 ◽  
Author(s):  
Haluk Aritürk
Keyword(s):  
Local Field ◽  
Principal Series ◽  
Roots Of Unity ◽  
Composition Series ◽  
Covering Group ◽  
Series Representations ◽  
Principal Series Representations

In this paper, we study the composition series of certain principal series representations of the three-fold metaplectic covering group of SL(2, K), where K is a non-archimedean local field. These representations are parametrized by unramified characters μ(x) = |x|s of K× and characters ω of the group of third roots of unity.

Computation of the norm factor group over Henselian fields and tame Brauer group of generalized local fields

2015 ◽  
Vol 14 (08) ◽  
pp. 1550134
Author(s):  
Mehran Motiee
Keyword(s):  
Abelian Group ◽  
Local Field ◽  
Finite Extension ◽  
Factor Group ◽  
Local Fields ◽  
Brauer Group ◽  
Divisible Abelian Group

Let F be a Henselian field. For a finite extension K of F, the norm factor group [Formula: see text] is computed. As an application, structure of the tame Brauer group of a generalized local field is determined. In particular, we observe that every torsion divisible abelian group is realizable as the tame Brauer group of a generalized local field.

scholarly journals Solving a fixed number of equations over finite groups

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Philipp Nuspl
Keyword(s):  
Abelian Group ◽  
Finite Groups ◽  
Abelian Groups ◽  
Single Equation ◽  
Fixed Number ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Semidirect Products ◽  
Equations Over Groups ◽  
Systems Of Polynomial Equations

AbstractWe investigate the complexity of solving systems of polynomial equations over finite groups. In 1999 Goldmann and Russell showed $$\mathrm {NP}$$ NP -completeness of this problem for non-Abelian groups. We show that the problem can become tractable for some non-Abelian groups if we fix the number of equations. Recently, Földvári and Horváth showed that a single equation over groups which are semidirect products of a p-group with an Abelian group can be solved in polynomial time. We generalize this result and show that the same is true for systems with a fixed number of equations. This shows that for all groups for which the complexity of solving one equation has been proved to be in $$\mathrm {P}$$ P so far, solving a fixed number of equations is also in $$\mathrm {P}$$ P . Using the collecting procedure presented by Horváth and Szabó in 2006, we furthermore present a faster algorithm to solve systems of equations over groups of order pq.

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