| Title: | On bilinear maps on matrices with applications to commutativity preservers |
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| Authors: | ID Brešar, Matej (Author)
ID Šemrl, Peter (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.jalgebra.2005.11.002
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | PEF - Faculty of Education
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| Abstract: | Naj bo ▫$M_n$▫ algebra vseh ▫$n times n$▫ matrik nad komutativnim enotskim kolobarjem ▫$mathcal{C}$▫, and naj bo ▫$mathcal{L}$▫ modul nad ▫$mathcal{C}$▫. Podane so različne karakterizacije bilinearnih preslikav ▫${,.,,,.,}: M_n times M_n to mathcal{L}$▫ z lastnostjo, da je ▫${x,y} = 0$▫, kadarkoli ▫$x$▫ in ▫$y$▫ komutirata. Kot glavno aplikacijo dobimo dokončno rešitev problema opisa (ne nujno bijektivnih) linearnih ohranjevalcev komutativnosti iz ▫$M_n$▫ v ▫$M_n$▫ za primer, ko je ▫$mathcal{C}$▫ poljubno polje; še več, enak opis velja v vsaki končno razsežni centralni enostavni algebri. |
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| Keywords: | matematika, matrična algebra, bilinearna preslikava, ohranjevalec komutativnosti, funkcijska identiteta, neasociativni produkt, centralna enostavna algebra, mathematics, matrix algebra, central simple algebra, functional identity, nonassociative product, Lie-admissible algebra, commutativity preserving map |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 803-837 |
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| Numbering: | Vol. 301, no 2 |
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| PID: | 20.500.12556/DKUM-51552  |
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| UDC: | 512.643 |
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| ISSN on article: | 0021-8693 |
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| COBISS.SI-ID: | 13984857 |
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| NUK URN: | URN:SI:UM:DK:13LDPGMF |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1315 |
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| Downloads: | 100 |
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| Metadata: |    |
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| Categories: | Misc.
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