Chooi, Wai Leong and Kwa, Kiam Heong and Tan, Li Yin (2020) Commuting maps on rank k triangular matrices. Linear & Multilinear Algebra, 68 (5). pp. 1021-1030. ISSN 03081087, DOI https://doi.org/10.1080/03081087.2018.1527281.
Full text not available from this repository.Abstract
Let n >= 2 be an integer and let F be a field with vertical bar F vertical bar >= 3. Let T-n(F) be the ring of n x n upper triangular matrices over F with centre Z. Fixing an integer 2 <= k <= n,we prove thatan additive map psi: T-n (F) -> T-n(F) satisfies A psi (A) = psi(A)A for all rank k matrices A is an element of T-n(F) if and only if there exist an additive map mu: T-n(F) -> Z, Z is an element of Z and alpha is an element of F in which alpha = 0 when vertical bar F vertical bar > 3 or k < n such that psi(A) = ZA + mu(A) alpha(a(11) + a(nn))E-1n for all A = (a(ij)) is an element of T-n(F). Here, E-1n is an element of T-n(F) is the matrix whose (1, n)th entry is one and zeros elsewhere.
| Item Type: | Article |
|---|---|
| Funders: | None |
| Uncontrolled Keywords: | Commuting map; Additive map; Triangular matrix; Rank; Functional identity |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms Zaharah Ramly |
| Date Deposited: | 04 Nov 2024 07:56 |
| Last Modified: | 04 Nov 2024 07:56 |
| URI: | http://eprints.um.edu.my/id/eprint/36699 |
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