Strong commutativity preserving additive maps on rank k triangular matrices
Document Type
Article
Publication Date
1-1-2024
Abstract
Let n >= 2 be an integer and let T-n(D) be the ring of nxn upper triangular matrices over a division ring D with centre Z(T-n(D)). In this paper, we characterize additive maps psi:T-n(D)-> T-n(D) satisfying psi(A),psi(B)]-A,B]is an element of Z(T-n(D)) for all A,B is an element of T-n(D). We then deduce from this result a complete characterization of strong commutativity preserving additive maps psi:T-n(D)-> T-n(D) on rank k upper triangular matrices, where 1 <= k <= n is a fixed integer such that k&NOTEQUexpressionL;n when |D|=2.
Keywords
Strong commutativity preserving map, upper triangular matrix, division ring, functional identity, linear preserver problem
Divisions
MathematicalSciences
Funders
Ministry of Education, Malaysia [Grant No: FRGS/1/2022/STG06/UM/02/7]
Publication Title
Linear & Multilinear Algebra
Volume
72
Issue
1
Publisher
Taylor & Francis Ltd
Publisher Location
2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND