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Functional identities of one variableBrešar, Matej ; Špenko, ŠpelaNaj bo ▫$A$▫centralno zaprta praalgebra nad poljem ▫$k$▫ s karakteristiko 0 in naj bo ▫$q: A \to A$▫ sled ▫$d$▫-linearne preslikave (tj. ▫$q(x) = (x, \dots , x)$▫, kjer je ▫$M: A^d \to A$▫ ... ▫$d$▫-linearna preslikava). Če je ▫$[q(x),x] = 0$▫ za vsak ▫$x \in A$▫, potem je ▫$q$▫ standardne oblike. Za neskončno razsežne algebre in algebre dimenzij ▫$>d^2$▫ so to dokazali Lee, Lin, Wang, in Wong leta 1997. V članku obdelamo primer, ko je dimenzija ▫$\le d^2$▫. S pomočjo tega rezultata razrešimo splošne funkcijske identitete ene spremenljivke na ▫$A$▫. Natančneje, opisane so sledi ▫$d$▫-linearnih preslikav ▫$q_i: A \to A$▫ z lastnostjo ▫$\sum_{i=0}^m x^i q_i(x)x^{m-i} \in k$▫ za vsak ▫$x \in A$▫.Source: Journal of algebra. - ISSN 0021-8693 (Vol. 401, 2014, str. 234-244)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 16842329
Author
Brešar, Matej |
Špenko, Špela
Topics
matematika |
algebra |
funkcijske identitete |
komutirajoče preslikave |
matrična algebra |
centralno zaprta algebra |
CayleyHamiltonov izrek |
prirejenka |
mathematics |
algebra |
functional identities |
commuting maps |
matrix algebra |
centrally closed prime algebra |
CayleyHamilton theorem |
adjugate matrix |
integrally closed domain
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Brešar, Matej | 08721 |
Špenko, Špela | 33617 |
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