1. Jordan maps and zero Lie product determined algebrasMatej Brešar, 2022, izvirni znanstveni članek Opis: 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.
Ključne besede: bilinear map, zero Lie product determined algebra, derivation, Jordan derivation, Jordan homomorphism, functional identity
Objavljeno v DKUM: 18.08.2023; Ogledov: 421; Prenosov: 46
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2. Cui, Jianlian; Hou, Jinchuan: Linear maps on von Neumann algebras preserving zero products of tr-rank. (English). - [J] Bull. Aust. Math. Soc. 65, No.1, 79-91(2002). [ISSN 0004-9727]Matej Brešar, 2005, recenzija, prikaz knjige, kritika Ključne besede: matematika, teorija operatorjev, linearni ohranjevalci, von Neumannove algebre, ničelni produkt, mathematics, operator theory, Banach algebras, linear preservers, von Neumann algebra, zero product, tr-rank
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6. Miura, Takeshi (J-YAMATS-AM); Oka, Hirokazu (J-IBARE); Hirasawa, Go (J-IBARE); Takahasi, Sin-Ei (J-YAMATS-AM): Superstability of multipliers and ring derivations on Banach algebras. (English summary). - Banach J. Math. Anal. 1 (2007), no. 1, 125--130Matej Brešar, 2008, recenzija, prikaz knjige, kritika Objavljeno v DKUM: 10.07.2015; Ogledov: 493; Prenosov: 45
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8. Martindale, Wallace S. III: Lie maps in prime rings: a personal perspective. (English). - [A] Chebotar, Mikhail (ed.) et al., Rings and nearrings. Proceedingsof the international conference of algebra in memory of Kostia Beidar, Tainan, Taiwan, March 6--12, 2005. Berlin: Walter de Gruyter. 95-110 (2007). [ISBN 978-3-11-019952-9/hbk]Matej Brešar, 2008, recenzija, prikaz knjige, kritika Objavljeno v DKUM: 10.07.2015; Ogledov: 374; Prenosov: 35
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9. Dobovišek, M.; Kuzma, B.; Lešnjak, G.; Li, C.K.; Petek, T.: Mappings that preserve pairs of operators with zero triple Jordan product. (English). - [J] Linear Algebra Appl. 426, No. 2-3, 255-279 (2007). [ISSN 0024-37951đMatej Brešar, 2008, recenzija, prikaz knjige, kritika Objavljeno v DKUM: 10.07.2015; Ogledov: 956; Prenosov: 44
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