20.500.12556/RUP-621
Rank-permutable additive mappings
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.
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.
mathematics
linearna algebra
matrix algebra
rank
permutation
additive preservers
matematika
linearna algebra
matrična algebra
aditivni ohranjevalci
rang
permutacija
true
true
false
Angleški jezik
Slovenski jezik
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2013-10-15 12:05:02
2013-10-15 12:05:02
2024-03-01 11:56:07
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2006
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str. 607-616
iss. 2-3
Vol. 414
2006
0000-00-00
NiDoloceno
NiDoloceno
NiDoloceno
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0000-00-00
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0024-3795
511.643
13949273
http://dx.doi.org/10.1016/j.laa.2005.11.003
1
https://repozitorij.upr.si/Dokument.php?lang=slv&id=621
Inštitut Andrej Marušič
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