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Title:Rank-permutable additive mappings
Authors:Alieva, Anna A. (Author)
Guterman, Aleksandr Èmilevič (Author)
Kuzma, Bojan (Author)
Files:URL http://dx.doi.org/10.1016/j.laa.2005.11.003
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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.
Keywords:mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers
Year of publishing:2006
Number of pages:str. 607-616
Numbering:Vol. 414, iss. 2-3
ISSN:0024-3795
UDC:511.643
COBISS_ID:13949273 Link is opened in a new window
Views:2632
Downloads:85
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Secondary language

Language:Slovenian
Abstract:Bodi ▫$\sigma$▫ netrivialna permutacija na ▫$k$▫ elementih. Klasificiramo vse aditivne bijekcije ▫$T:M_n(F)\to M_n(F)$▫, ki ohranjajo ▫$\sigma$▫-rang permutabilnost na algebri matrik s koeficienti iz komutativnega obsega ▫$F$▫ ničelne karakteristike. Natančneje: Čim urejena ▫$k$▫-terka matrik ▫$(A_1,..,A_k)$▫ ustreza pogoju ▫$\rm{rk}(A_1...A_k) = \rm{rk}(A_{\sigma(1)} ... A_{\sigma(k)})$▫ potem isto velja za preslikano ▫$k$▫-terko ▫$(T(A_1),..,T(A_k))$▫. Če se ▫$\sigma$▫-rang permutabilnost ohranja v obeh smereh, lahko predpostavko o bijektivnosti omilimo.
Keywords:matematika, linearna algebra, matrična algebra, aditivni ohranjevalci, rang, permutacija

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