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Abstract
Let $A$ be a finitedimensional algebra over the rational number field $\Bbb Q$. A subring $\Gamma$ with the same unit element is called an order if $\Gamma$ is a finitely generated $\Bbb Z$submodule such that $\Gamma$ contains a $\Bbb Q$basis of $A$. Although the unit group $U(\Gamma)$ of $\Gamma$ is finitely generated, the determination of a finite set of generators seems to be a problem beyond reach. The authors give a survey of recent accomplishments on the following topics concerning $U(\Gamma)$: (1) special subgroups; (2) generators for a subgroup of finite index; (3) orders in quaternion algebras.
Original language  English 

Pages (fromto)  119136 
Number of pages  18 
Journal  Groups, Rings and Group Rings 
Issue number  248 
Publication status  Published  2006 
Keywords
 units
 orders
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Dive into the research topics of 'Units in Noncommutative Orders'. Together they form a unique fingerprint.Activities
 1 Talk or presentation at a conference

Groups, Rings and Group Rings
Ann Dooms (Speaker)
26 Jul 2004 → 31 Jul 2004Activity: Talk or presentation › Talk or presentation at a conference