Anna A. Alieva (Author), Aleksandr Èmilevič Guterman (Author), Bojan Kuzma (Author)

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;mathematics;matrix algebra;rank;permutation;additive preservers;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UP - University of Primorska
UDC: 511.643
COBISS: 13949273 Link will open in a new window
ISSN: 0024-3795
Views: 3198
Downloads: 89
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Other data

Secondary language: Slovenian
Secondary title: Aditivni ohranjevalci rang-permutabilnosti
Secondary 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.
Secondary keywords: matematika;linearna algebra;matrična algebra;aditivni ohranjevalci;rang;permutacija;
Type (COBISS): Not categorized
Pages: str. 607-616
Volume: ǂVol. ǂ414
Issue: ǂiss. ǂ2-3
Chronology: 2006
ID: 1472649