scholarly journals Nonlinear Jordan Derivable Mappings of Generalized Matrix Algebras by Lie Product Square-Zero Elements

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xiuhai Fei ◽  
Haifang Zhang
Keyword(s):  
Matrix Algebra ◽  
Matrix Algebras ◽  
Generalized Matrix ◽  
Generalized Matrix Algebra

The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping Δ of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation δ and an additive antiderivation f . Moreover, δ and f are uniquely determined.

scholarly journals σ-derivations on generalized matrix algebras

2020 ◽  
Vol 28 (2) ◽  
pp. 115-135
Author(s):  
Aisha Jabeen ◽  
Mohammad Ashraf ◽  
Musheer Ahmad
Keyword(s):  
Commutative Ring ◽  
Matrix Algebra ◽  
Morita Context ◽  
Matrix Algebras ◽  
Generalized Matrix ◽  
Generalized Matrix Algebra

AbstractLet 𝒭 be a commutative ring with unity, 𝒜, 𝒝 be 𝒭-algebras, 𝒨 be (𝒜, 𝒝)-bimodule and 𝒩 be (𝒝, 𝒜)-bimodule. The 𝒭-algebra 𝒢 = 𝒢(𝒜, 𝒨, 𝒩, 𝒝) is a generalized matrix algebra defined by the Morita context (𝒜, 𝒝, 𝒨, 𝒩, ξ𝒨𝒩, Ω𝒩𝒨). In this article, we study Jordan σ-derivations on generalized matrix algebras.

scholarly journals The First Hochschild Cohomology of Square Algebras With it's Stability

2017 ◽  
Vol 9 (4) ◽  
pp. 200
Author(s):  
Feysal Hassani ◽  
Negin Salehi Oroozaki
Keyword(s):  
Significant Role ◽  
Matrix Algebra ◽  
Hochschild Cohomology ◽  
Generalized Matrix ◽  
Generalized Matrix Algebra ◽  
Special Case

In this paper, we study on a special case of generalized matrix algebra that we call it square algebra. According to that Hochschild cohomology play a significant role in Geometry for example in orbifolds, we study the first Hochschild cohomology of the square algebra the vanishing of its.

scholarly journals More on Lie derivations of a generalized matrix algebra

2018 ◽  
Vol 19 (1) ◽  
pp. 385 ◽  
Author(s):  
A.H. Mokhtari ◽  
H.R. Ebrahimi Vishki
Keyword(s):  
Matrix Algebra ◽  
Generalized Matrix ◽  
Generalized Matrix Algebra ◽  
Lie Derivations

Theory of Adjustments by Least Squares

1965 ◽  
Vol 19 (1) ◽  
pp. 42-63
Author(s):  
L. A. Gale
Keyword(s):  
Least Squares ◽  
Linear Relationship ◽  
Matrix Algebra ◽  
Covariance Matrices ◽  
Transformation Matrix ◽  
Correlated Observations ◽  
Generalized Matrix ◽  
Independent Observations ◽  
Singular Transformation ◽  
Generalized Matrix Algebra

The concepts of least squares adjustments and the relationships between various types of adjustment are presented in terms of generalized matrix algebra. By developments based on the variance law for independent observations and the linear relationship between independent and correlated observations, variance-covariance matrices and the corresponding weight matrices are developed. The use of generalized matrix algebra permits the derivation of weight matrices from singular, variance-covariance matrices by inversion of the latter matrices. A singular transformation matrix for the elimination of superfluous parameters from observation equations prior to adjustment is presented.

scholarly journals On Modular Representation Algebras and a Class of Matrix Algebras

1982 ◽  
Vol 33 (3) ◽  
pp. 351-355 ◽  
Author(s):  
J-C. Renaud
Keyword(s):  
Tensor Product ◽  
Cyclic Group ◽  
Prime Order ◽  
Matrix Algebra ◽  
Modular Representation ◽  
Complex Field ◽  
Matrix Algebras ◽  
Direct Sum ◽  
Standard Operations

AbstractLet G be a cyclic group of prime order p and K a field of characteristic p. The set of classes of isomorphic indecomposable (K, G)-modules forms a basis over the complex field for an algebra p (Green, 1962) with addition and multiplication being derived from direct sum and tensor product operations.Algebras n with similar properties can be defined for all n ≥ 2. Each such algebra is isomorphic to a matrix algebra Mn of n × n matrices with complex entries and standard operations. The characters of elements of n are the eigenvalues of the corresponding matrices in Mn.

scholarly journals Zero Triple Product Determined Matrix Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hongmei Yao ◽  
Baodong Zheng
Keyword(s):  
Linear Operator ◽  
Matrix Algebra ◽  
Triple Product ◽  
Unital Algebra ◽  
Matrix Algebras ◽  
Unital Ring ◽  
Jordan Triple Product

LetAbe an algebra over a commutative unital ringC. We say thatAis zero triple product determined if for everyC-moduleXand every trilinear map{⋅,⋅,⋅}, the following holds: if{x,y,z}=0wheneverxyz=0, then there exists aC-linear operatorT:A3⟶Xsuch thatx,y,z=T(xyz)for allx,y,z∈A. If the ordinary triple product in the aforementioned definition is replaced by Jordan triple product, thenAis called zero Jordan triple product determined. This paper mainly shows that matrix algebraMn(B),n≥3, whereBis any commutative unital algebra even different from the above mentioned commutative unital algebraC, is always zero triple product determined, andMn(F),n≥3, whereFis any field with chF≠2, is also zero Jordan triple product determined.

scholarly journals Unital locally matrix algebras and Steinitz numbers

2019 ◽  
Vol 19 (09) ◽  
pp. 2050180
Author(s):  
Oksana Bezushchak ◽  
Bogdana Oliynyk
Keyword(s):  
Matrix Algebra ◽  
Finite Collection ◽  
Matrix Algebras ◽  
Number Formula ◽  
Unit Formula

An [Formula: see text]-algebra [Formula: see text] with unit [Formula: see text] is said to be a locally matrix algebra if an arbitrary finite collection of elements [Formula: see text] from [Formula: see text] lies in a subalgebra [Formula: see text] with [Formula: see text] of the algebra [Formula: see text], that is isomorphic to a matrix algebra [Formula: see text], [Formula: see text]. To an arbitrary unital locally matrix algebra [Formula: see text], we assign a Steinitz number [Formula: see text] and study a relationship between [Formula: see text] and [Formula: see text].

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