Rank-permutable additive mappings

A. A. Alieva; A. E. Guterman; B. Kuzma

doi:10.1016/j.laa.2005.11.003

Rank-permutable additive mappings

A. A. Alieva, A. E. Guterman, B. Kuzma

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let σ be a fixed non-identical permutation on k elements. Additive bijections T on the matrix algebra Mn(F) over a field F of characteristic zero, with the property that rk(A1⋯Ak)=rkAσ(1)⋯Aσ(k) implies the same condition on the T images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.

Original language	English
Pages (from-to)	607-616
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	414
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2005.11.003
State	Published - 15 Apr 2006
Externally published	Yes

Keywords

Additive preservers
Matrix algebra
Permutation
Rank

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10.1016/j.laa.2005.11.003

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AB - Let σ be a fixed non-identical permutation on k elements. Additive bijections T on the matrix algebra Mn(F) over a field F of characteristic zero, with the property that rk(A1⋯Ak)=rkAσ(1)⋯Aσ(k) implies the same condition on the T images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.

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KW - Matrix algebra

KW - Permutation

KW - Rank

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -

Rank-permutable additive mappings

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Keywords

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