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Torsion units in integral group rings of Conway simple groups
Zassenhaus conjecture torsion unit partial augmentation
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2011/2/24
Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and C...
Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $\Lambda[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions
11R23 Iwasawa Theory 11R27 Units
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2010/12/9
For = Zp[[T ]], the ring of formal power series in one variable, the structure of the finitely generated - torsion modules is a main concern of Iwasawa theory. In this first part of Snoqit1 we inv...
On rings of integers generated by their units
sums of units generated by units
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2010/11/29
We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true that every number field has a finite extension L such that the ring of integers of L is generated by its un...
Group rings whose group of units is hyperbolic
hyperbolic group group ring unit group
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2010/12/6
We study those group rings whose group of units is hyperbolic.Let (X, ) be a metric space with metric . For any a, b, c ∈ X, the Gromov product hb, cia of b and c with respect to a ∈ X is defined as...
Exchange rings generated by their units
置换环 本原分式环 强$\pi$正则环
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2007/12/10
假设$R$为本原分式Artinian环,证明了有$u\in U(R)$使得$1_R\pm u\in U(R)$ 当且仅当对任何$a\in R$, 有$u\in U(R)$使得$a\pm u\in U(R)$. 进一步，证明了 对任何$A\in M_n(R)(n\geq 2)$, 有$U\in GL_n(R)$ 使得$A\pm U\in GL_n(R)$. 作为应用得到了强$\pi$正则环中任何元素...