| Title: | Rank-permutable additive mappings |
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| Authors: | ID Alieva, Anna A. (Author)
ID Guterman, Aleksandr Èmilevič (Author)
ID Kuzma, Bojan (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.laa.2005.11.003
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | Let ▫$\sigma$▫ be a fixed non-identical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ 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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| Keywords: | mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 607-616 |
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| Numbering: | Vol. 414, iss. 2-3 |
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| PID: | 20.500.12556/RUP-621  |
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| ISSN: | 0024-3795 |
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| UDC: | 511.643 |
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| COBISS.SI-ID: | 13949273 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 3482 |
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| Downloads: | 89 |
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