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Characterizations of Lie centralizers of generalized matrix algebras
Communications in Algebra, 2023Let G be a generalized matrix algebra. A linear map ϕ:G→G is said to be a left (right) Lie centralizer at E∈G if ϕ([S,T])=[ϕ(S),T] (ϕ([S,T])=[S,ϕ(T)]) holds for all S,T∈G with ST = E. ϕ is of a standard form if ϕ(A)=ZA+γ(A) for all A∈G, where Z is in the
Lei Liu, Kaitian Gao
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Lie centralizers at the zero products on generalized matrix algebras
, 2021Let [Formula: see text] be a 2-torsion free unital generalized matrix algebra, and [Formula: see text] be a linear map satisfying [Formula: see text] In this paper, we study the structure of [Formula: see text] and under some mild conditions on [Formula:
B. Fadaee, H. Ghahramani
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On nonlinear Lie centralizers of generalized matrix algebras
Linear and multilinear algebra, 2020The aim of the paper is to give a description of nonlinear Lie centralizers for a certain class of generalized matrix algebras. The result is then applied to some full matrix algebras and triangular algebras.
Lei Liu
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Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms
Algebra Colloquium, 2022Let [Formula: see text] be a ring with an automorphism [Formula: see text] of order two. We introduce the definition of [Formula: see text]-centrosymmetric matrices. Denote by [Formula: see text] the ring of all [Formula: see text] matrices over [Formula: see text], and by [Formula: see text] the set of all [Formula: see text]-centrosymmetric [Formula:
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Characterizations of Lie triple derivations on generalized matrix algebras
, 2020Let be a commutative ring with unity and be a generalized matrix algebra. In this article, we give the structure of Lie triple derivation on a generalized matrix algebra and prove that under certain appropriate assumptions on is proper, i.e., where δ is ...
M. Ashraf, Mohd Shuaib Akhtar
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On a generalized Jordan form of an infinite upper triangular matrix
Linear and multilinear algebra, 2021Any square matrix over an algebraically closed field has a Jordan normal form. In this paper, we prove that every infinite upper triangular matrix over an arbitrary field has a generalized infinite Jordan normal form.
A. Kostic +3 more
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Generalized matrix completion and algebraic natural proofs
Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk (Proc. of the 49th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 653–664, 2017) and independently by Grochow, Kumar, Saks and Saraf (CoRR, abs/1701.01717, 2017) as an attempt to transfer Razborov and Rudich’s famous barrier result (J. Comput. Syst. Sci., 55(
Bläser, M. +3 more
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Extremal generalized centralizers in matrix algebras
Communications in Algebra, 2018We describe matrices with extremal generalized centralizers over algebraically closed fields.
Gregor Dolinar +3 more
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General Algebra and Linear Transformations Preserving Matrix Invariants
Journal of Mathematical Sciences, 2005The theory of linear transformations preserving matrix invariants dates back to 1987, when Georg Frobenius characterized bijective linear transformations preserving the determinant for matrices over the field of complex numbers. During the past century this theory was intensively developed in different directions.
Guterman, A. E., Mikhalev, A. V.
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Matrix generalized (θ, ϕ)-derivations on matrix Banach algebras
Mathematica Slovaca, 2018Abstract We introduce the concept of matrix generalized (θ, ϕ)-derivations on matrix normed algebras, and prove the Hyers-Ulam stability of matrix generalized (θ, ϕ)-derivations on matrix Banach algebras.
Batool, Afshan +2 more
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