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Rank-permutable additive mappingsAleksandr Èmilevič Guterman,
Anna A. Alieva,
Bojan Kuzma, 2006, original scientific article
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.
Found in: osebi
Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers
Published: 15.10.2013; Views: 2632; Downloads: 85
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