Commuting Maps of Triangular Algebras

By W. Cheung. 2001

192 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5b4212a1e7772cae965a6e438a13a7eece35f264

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Dominik Benkovič
2. Xiaomin Tang
3. Yiqiu Du
4. Yu Wang
5. Feng Wei
6. Jianhua Zhang
7. Matej Breˇsar
8. W. Jing

In Computational Theory and Mathematics

1. Dominik Benkovič
2. Xiaomin Tang
3. Matej Breˇsar
4. Xuehan Cheng
5. W. Jing
6. Yanbo Li
7. Jianhua Zhang
8. Yiqiu Du

In Geometry and Topology

1. Dominik Benkovič
2. Xiaomin Tang
3. Yiqiu Du
4. Yu Wang
5. Feng Wei
6. Jianhua Zhang
7. Matej Breˇsar
8. W. Jing

Citations in the corpus

• On Jordan Derivations of Triangular Algebras (2007, background): “under the usual matrix operations, where A and B are two algebras over a commutative ring R, and M is an (A,B)-bimodule which is faithful as a left A-module and also as a right B-module (see [3]).”
• Biderivations of finite-dimensional complex simple Lie algebras (2016, background): “Then many scholars study commuting maps on all kinds of algebra structures [1, 3, 4, 7, 8, 11, 13, 16, 18, 20].”
• Commuting traces and commutativity preserving maps on triangular algebras (2004, background): “Recently, Cheung [27, Theorem 2] proved that each commuting linear map ofA = Tri(A,M,B) is proper if πA(Z(A)) = Z(A) (or A = [A,A]), πB(Z(A)) = Z(B) (or B = [B,B]), and Z(A) = {a ⊕ b | a ∈ Z(A), b ∈ Z(B), am0 = m0b} for somem0 ∈ M.”
• Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras (2017, background): “About the recent articles on commuting maps we can reference [3, 6, 7, 11, 13, 16, 22, 32, 35, 36].”
• Biderivations and linear commuting maps on simple generalized Witt algebras over a field (2016, unknown): “(see [3, 6, 7, 9, 11, 12, 16, 17, 18, 19, 21]).”
• Lie Derivations of Triangular Algebras (2003, background): “One may refer to [2] (also see [3]) for a general description of triangular algebras.”
• Lie triple derivations of unital algebras with idempotents (2015, background): “(43) The concept of an element m0 on triangular algebras was introduced by Cheung [22] and it proved to be very useful at his studies of commuting mappings on triangular algebras.”
• Semi-centralizing maps of generalized matrix algebras☆ (2012, background): “Cheung initially studied commuting maps of matrix algebras in [4].”
• Biderivations and Commuting Linear Maps on Lie Algebras (2018, unknown): “It is a modification of an example from [7].”
• Lie derivations of generalized matrix algebras (2012, background): “Cheung [5] initiated the study ofmapping problems on triangular algebras.”
• COMMUTING MAPS: A SURVEY (2004, methodology): “In [82] this example was used to show that not every additive commuting map of the socalled triangular algebra is of the form (6).”