| 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: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | PEF - Faculty of Education
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| Abstract: | Let ▫$M_n$▫ be the algebra of all ▫$n times n$▫ matrices over a commutative unital ring ▫$mathcal{C}$▫, and let ▫$mathcal{L}$▫ be a ▫$mathcal{C}$▫-module. Various characterizations of bilinear maps ▫${,.,,,.,}: M_n times M_n to mathcal{L}$▫ with the property that ▫${x,y} = 0$▫ whenever ▫$x$▫ any ▫$y$▫ commute are given. As the main application of this result we obtain the definitive solution of the problem of describing (not necessarily bijective) commutativity preserving linear maps from ▫$M_n$▫ into ▫$M_n$▫ for the case where ▫$mathcal{C}$▫ is an arbitrary field; moreover, this description is valid in every finite dimensional central simple algebra. |
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| Keywords: | mathematics, matrix algebra, central simple algebra, functional identity, nonassociative product, Lie-admissible algebra, commutativity preserving map |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publisher: | Elsevier |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 803-837 |
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| Numbering: | Letn. 301, št. 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: | 1496 |
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| Downloads: | 106 |
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| Metadata: |    |
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| Categories: | Misc.
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