scholarly journals A Class of Nonlinear Nonglobal Semi-Jordan Triple Derivable Mappings on Triangular Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiuhai Fei ◽  
Haifang Zhang
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Nest Algebra ◽  
Triangular Algebra ◽  
Triangular Matrix Algebra ◽  
Free Block ◽  
Upper Triangular Matrix ◽  
Triangular Algebras ◽  
Torsion Free

In this paper, we proved that each nonlinear nonglobal semi-Jordan triple derivable mapping on a 2-torsion free triangular algebra is an additive derivation. As its application, we get the similar conclusion on a nest algebra or a 2-torsion free block upper triangular matrix algebra, respectively.

scholarly journals The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices

2021 ◽  
Vol 29 (2) ◽  
pp. 183-186
Author(s):  
Thiago Castilho de Mello
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Infinite Field ◽  
Arbitrary Degree ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Triangular Matrix Algebra ◽  
Upper Triangular Matrix ◽  
Multilinear Polynomials

Abstract We describe the images of multilinear polynomials of arbitrary degree evaluated on the 3×3 upper triangular matrix algebra over an infinite field.

scholarly journals Nonlinear maps preserving Lie products on triangular algebras

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Weiyan Yu
Keyword(s):  
Triangular Matrix ◽  
Matrix Algebras ◽  
Triangular Algebra ◽  
Nest Algebras ◽  
Upper Triangular Matrix ◽  
Nonlinear Maps ◽  
Triangular Algebras

AbstractIn this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.

scholarly journals DECOMPOSITION OF JORDAN AUTOMORPHISMS OF TRIANGULAR MATRIX ALGEBRA OVER COMMUTATIVE RINGS

2010 ◽  
Vol 52 (3) ◽  
pp. 529-536 ◽  
Author(s):  
XING TAO WANG ◽  
YUAN MIN LI
Keyword(s):  
Commutative Ring ◽  
Matrix Algebra ◽  
Triangular Matrix ◽  
Commutative Rings ◽  
Graph Automorphism ◽  
Triangular Matrix Algebra ◽  
Inner Automorphism

AbstractLet Tn+1(R) be the algebra of all upper triangular n+1 by n+1 matrices over a 2-torsionfree commutative ring R with identity. In this paper, we give a complete description of the Jordan automorphisms of Tn+1(R), proving that every Jordan automorphism of Tn+1(R) can be written in a unique way as a product of a graph automorphism, an inner automorphism and a diagonal automorphism for n ≥ 1.

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