Rank-permutable additive mappings

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Title:	Rank-permutable additive mappings
Authors:	ID Alieva, Anna A. (Author) ID Guterman, Aleksandr Èmilevič (Author) ID Kuzma, Bojan (Author)
Files:	http://dx.doi.org/10.1016/j.laa.2005.11.003
Language:	English
Work type:	Not categorized
Typology:	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
PID:	20.500.12556/RUP-621
ISSN:	0024-3795
UDC:	511.643
COBISS.SI-ID:	13949273
Publication date in RUP:	15.10.2013
Views:	4924
Downloads:	93
Metadata:
:	ALIEVA, Anna A., GUTERMAN, Aleksandr Èmilevič and KUZMA, Bojan, 2006, Rank-permutable additive mappings. [online]. 2006. Vol. 414, no. 2–3, p. 607–616. [Accessed 13 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.laa.2005.11.003 Copy citation

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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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