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1. CMB 2010 (vol 54 pp. 237)
The Structure of the Unit Group of the Group Algebra ${\mathbb{F}}_{2^k}D_{8}$
Let $RG$ denote the group ring of the group $G$ over
the ring $R$. Using an isomorphism between $RG$ and a
certain ring of $n \times n$ matrices in conjunction with other
techniques, the structure of the unit group of the group algebra
of the dihedral group of order $8$ over any
finite field of chracteristic $2$ is determined in
terms of split extensions of cyclic groups.
Categories:16U60, 16S34, 20C05, 15A33 |
2. CMB 2006 (vol 49 pp. 96)
Roots of Simple Modules We introduce roots of indecomposable modules over group algebras of finite groups,
and we investigate some of their properties. This allows us to correct an error
in Landrock's book which has to do with roots of simple modules.
Categories:20C20, 20C05 |
3. CMB 2005 (vol 48 pp. 80)
Trivial Units for Group Rings with $G$-adapted Coefficient Rings For each finite group $G$ for which the integral group ring
$\mathbb{Z}G$ has only trivial units, we give ring-theoretic
conditions for a commutative ring $R$ under which the group ring
$RG$ has nontrivial units. Several examples of rings satisfying
the conditions and rings not satisfying the conditions are given.
In addition, we extend a well-known result for fields by showing
that if $R$ is a ring of finite characteristic and $RG$ has only
trivial units, then $G$ has order at most 3.
Categories:16S34, 16U60, 20C05 |