scholarly journals CONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS

2017 ◽  
Vol 20 (10) ◽  
pp. 84-90
Author(s):  
A.V. Polovinkina ◽  
T.V. Skoraya
Keyword(s):  
Symmetric Group ◽  
Free Algebra ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Base Field ◽  
Direct Sum ◽  
Zero Characteristic ◽  
Necessary And Sufficient ◽  
Relationship Of ◽  
The Relationship

This paper is devoted to the varieties of Leibnitz algebras over a field of zero characteristic. All information about the variety in case of zero characteristic of the base field is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with finite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sufficient condition for a finiteness of colength of variety of Leibnitz algebras.

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

scholarly journals Chaos for Cosine Operator Functions on Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Locally Compact Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Direct Sum ◽  
Cosine Operator ◽  
Weight Condition ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Necessary And Sufficient

Let1≤p<∞andGbe a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue spaceLp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.

scholarly journals Direct-sum decomposition of atomic and orthogonally complete rings

1970 ◽  
Vol 11 (3) ◽  
pp. 357-361 ◽  
Author(s):  
Alexander Abian
Keyword(s):  
Natural Number ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Image Position ◽  
Necessary And Sufficient

In this paper we give a necessary and sufficient condition for decomposition (as a direct sum of fields) of a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that . We would like to emphasize that in what follows R stands for a ring every element x of which satisfies (1).

scholarly journals Sifat-Sifat Representasi Indekomposabel The Properties of Indecomposable Representations

2019 ◽  
Vol 8 (3) ◽  
Author(s):  
Vika Yugi Kurniawan
Keyword(s):  
Vector Space ◽  
Directed Graph ◽  
Linear Mapping ◽  
Sufficient Condition ◽  
Paper Study ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Indecomposable Representations ◽  
Finite Set ◽  
Necessary And Sufficient

A directed graph is also called as a quiver  where  is a finite set of vertices,  is a set of arrows, and  are two maps from  to . A representation  of a quiver  is an assignment of a vector space  to each vertex  of  and a linear mapping  to each arrow.  We denote by  the direct sum of representasions  and  of a quiver  . A representation  is called indecomposable if  is not ishomorphic to a direct sum of non-zero representations. This paper study about the properties of indecomposable representations. These properties will be used to investigate the necessary and sufficient condition of indecomposable representations.

scholarly journals Generalized Bertrand Curves in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2199
Author(s):  
Chunxiao Zhang ◽  
Donghe Pei
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bertrand Curve ◽  
Necessary And Sufficient ◽  
The Relationship

We define a generalized lightlike Bertrand curve pair and a generalized non-lightlike Bertrand curve pair, discuss their properties and prove the necessary and sufficient condition of a curve which is a generalized lightlike or a generalized non-lightlike Bertrand curve. Moreover, we study the relationship between slant helices and generalized Bertrand curves.

scholarly journals Fuzzy Small Submodule and Jacobson -Radical

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Saifur Rahman ◽  
Helen K. Saikia
Keyword(s):  
Jacobson Radical ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Necessary And Sufficient ◽  
Quotient Modules ◽  
Small Submodule

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum. Fuzzy small submodules of a module are characterized in terms of fuzzy quotient modules. This characterization gives rise to some results on fuzzy coessential extensions. Finally, a relation between small -submodules and Jacobson -radical is established.

scholarly journals On Properties of ClassA(n)andn-Paranormal Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiaochun Li ◽  
Fugen Gao
Keyword(s):  
Positive Integer ◽  
Tensor Products ◽  
Unit Vector ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Paranormal Operator ◽  
Necessary And Sufficient

Letnbe a positive integer, and an operatorT∈B(ℋ)is called a classA(n)operator ifT1+n2/1+n≥|T|2andn-paranormal operator ifT1+nx1/1+n≥||Tx||for every unit vectorx∈ℋ, which are common generalizations of classAand paranormal, respectively. In this paper, firstly we consider the tensor products for classA(n)operators, giving a necessary and sufficient condition forT⊗Sto be a classA(n)operator whenTandSare both non-zero operators; secondly we consider the properties forn-paranormal operators, showing that an-paranormal contraction is the direct sum of a unitary and aC.0completely non-unitary contraction.

scholarly journals Rational valued and real valued projective characters of finite groups

1980 ◽  
Vol 21 (1) ◽  
pp. 23-28 ◽  
Author(s):  
J. F. Humphreys
Keyword(s):  
Symmetric Group ◽  
Finite Groups ◽  
General Information ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Character ◽  
Definition Of ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Spin Characters

It is well-known [3; V.13.7] that each irreducible complex character of a finite group G is rational valued if and only if for each integer m coprime to the order of G and each g ∈ G, g is conjugate to gm. In particular, for each positive integer n, the symmetric group on n symbols, S(n), has all its irreducible characters rational valued. The situation for projective characters is quite different. In [5], Morris gives tables of the spin characters of S(n) for n ≤ 13 as well as general information about the values of these characters for any symmetric group. It can be seen from these results that in no case are all the spin characters of S(n) rational valued and, indeed, for n ≥ 6 these characters are not even all real valued. In section 2 of this note, we obtain a necessary and sufficient condition for each irreducible character of a group G associated with a 2-cocycle α to be rational valued. A corresponding result for real valued projective characters is discussed in section 3. Section 1 contains preliminary definitions and notation, including the definition of projective characters given in [2].

scholarly journals Derivations on some (possibly non-separable) C*-algebras

1981 ◽  
Vol 22 (1) ◽  
pp. 43-56 ◽  
Author(s):  
J. P. Sproston
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Degree ◽  
C Algebras ◽  
Direct Sum ◽  
Necessary And Sufficient

In an important recent paper [4], G. A. Elliott has given a necessary and sufficient condition for every derivation on a separable C*-algebra with identity to be inner. Indeed, Elliott's condition has since been shown, by Akemann and Pedersen, to be equivalent to the C*-algebra being a finite direct sum of C*-algebras which are either homogeneous of finite degree or simple [8, Corollary 3.10].

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