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On locally complex algebras and low-dimensional Cayley-Dickson algebrasBrešar, Matej ; Šemrl, Peter ; Špenko, ŠpelaČlanek se prične s kratkima dokazoma klasičnih izrekov Frobeniusa in Zorna o asociativnih in alternativnih realnih obsegih. Ta dva izreka karakterizirata prve štiri Cayley-Dicksonove algebre. Zatem ... vpeljemo in obravnavamo razred realnih neasociativnih algeber, v katerih je vsaka podalgebra, generirana z neskalarnim elementom, izomorfna algebri kompleksnih števil. Imenujemo jih lokalno kompleksne algebre. Med drugim opišemo vse take algebre dimenzije največ 4. Naša glavna motivacija za vpeljavo lokalno kompleksnih algebre pa je dejstvo, da nam ta koncept omogoči razširitev izrekov Frobeniusa in Zorna, tako da vključuje tudi peto Cayley-Dicksonovo algebro, sedenione.Source: Journal of algebra. - ISSN 0021-8693 (Vol. 327, iss. 1, 2011, str. 107-125)Type of material - article, component partPublish date - 2011Language - englishCOBISS.SI-ID - 15758681
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Database name | Field | Year |
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Brešar, Matej | 08721 |
Šemrl, Peter | 05953 |
Špenko, Špela | 33617 |
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