Commuting maps on rank k triangular matrices
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...
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| Main Authors: | , , |
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| Format: | Article |
| Published: |
Taylor & Francis Ltd
2020
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| Subjects: | |
| Online Access: | http://eprints.um.edu.my/36699/ |
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| Summary: | 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. |
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