scholarly journals Zero triple product determined generalized matrix algebras

2015 ◽  
Vol 39 ◽  
pp. 139-155
Author(s):  
Dong HAN
Keyword(s):  
Triple Product ◽  
Matrix Algebras ◽  
Generalized Matrix

scholarly journals On Additivity of Jordan Higher Mappings on Generalized Matrix Algebras

2021 ◽  
pp. 1334-1343
Author(s):  
Rajaa C. Shaheen
Keyword(s):  
Triple Product ◽  
Matrix Algebras ◽  
Generalized Matrix ◽  
Definition Of

In this article, the additivity of higher multiplicative mappings, i.e., Jordan mappings, on generalized matrix algebras are studied. Also, the definition of Jordan higher triple product homomorphism is introduced and its additivity on generalized matrix algebras is studied.

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 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.

Characterizations of Lie triple derivations on generalized matrix algebras

2020 ◽  
Vol 48 (9) ◽  
pp. 3651-3660
Author(s):  
Mohammad Ashraf ◽  
Mohd Shuaib Akhtar
Keyword(s):  
Matrix Algebras ◽  
Generalized Matrix
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