Alternative algebras with the hyperbolic property
| Autor: | Juriaans, S. O., Milies, C. Polcino, Filho, A. C. Souza |
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| Rok vydání: | 2008 |
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| Druh dokumentu: | Working Paper |
| Popis: | We investigate the structure of an alternative finite dimensional $\Q$-algebra $\mathfrak{A}$ subject to the condition that for a $\Z$-order $\Gamma \subset \mathfrak{A}$, and thus for every $\Z$-order of $\mathfrak{A}$, the loop of units of $\U (\Gamma)$ does not contain a free abelian subgroup of rank two. In particular, we prove that the radical of such an algebra associates with the whole algebra. We also classify $RA$-loops $L$ for which $\mathbb{Z}L$ has this property. The classification for group rings is still an open problem. Comment: Third author's Ph.D. (parcial); generalization of those results for the non-associative case, 9 pps. Conf.: Geometry, Topology, Algebra and Number Theory, Steklov Math. Inst., Moscow-Russia (Aug, 2010); XVIII Latin American Colloquium of Algebra, S\~ao Paulo-Brazil (July, 2009); Algebras, Representation and Applications, Ubatuba-Brazil (aug., 2007); Group and Group Rings, Bedlewo-Poland (2005) |
| Databáze: | arXiv |
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