| Title: | Jordan maps and zero Lie product determined algebras |
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| Authors: | ID Brešar, Matej (Author) |
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| Files: |  Jordan_maps_and_zero_Lie_product_d-Bresar-2022.pdf (215,86 KB)
MD5: 47B27989CC78D92ADE84E7C2154EDA55
 https://journals.tubitak.gov.tr/math/vol46/iss5/5/
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | Let ▫$A$▫ be an algebra over a field ▫$F$▫ with ▫$\mathrm{char} (F) \ne 2$▫. If ▫$A$▫ is generated as an algebra by ▫$[[A,A],[A,A]]$▫, then for every skew-symmetric bilinear map ▫$\Phi:A \times A \to X$▫, where ▫$X$▫ is an arbitrary vector space over ▫$F$▫, the condition that ▫$\Phi(x^2,x)=0$▫ for all ▫$x \in A$▫ implies that ▫$\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$▫ for all ▫$x,y,z \in A$▫. This is applicable to the question of whether ▫$A$▫ is zero Lie product determined, and is also used in proving that a Jordan homomorphism from ▫$A$▫ onto a semiprime algebra ▫$B$▫ is the sum of a homomorphism and an antihomomorphism. |
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| Keywords: | bilinear map, zero Lie product determined algebra, derivation, Jordan derivation, Jordan homomorphism, functional identity |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2022 |
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| Year of publishing: | 2022 |
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| Number of pages: | str. 1691-1698 |
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| Numbering: | Letn. 46, št. SI-2 |
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| PID: | 20.500.12556/DKUM-85111  |
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| UDC: | 512.552 |
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| ISSN on article: | 1300-0098 |
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| COBISS.SI-ID: | 123459843 |
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| DOI: | 10.55730/1300-0098.3226 |
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| Publication date in DKUM: | 18.08.2023 |
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| Views: | 548 |
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| Downloads: | 53 |
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| Metadata: |    |
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| Categories: | Misc.
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