Trivial Units for Group Rings with $G$-adapted Coefficient Rings

[摘要] For each finite group $G$ for which the integral group ring$mathbb{Z}G$ has only trivial units, we give ring-theoreticconditions for a commutative ring $R$ under which the group ring$RG$ has nontrivial units. Several examples of rings satisfyingthe conditions and rings not satisfying the conditions are given.In addition, we extend a well-known result for fields by showingthat if $R$ is a ring of finite characteristic and $RG$ has onlytrivial units, then $G$ has order at most 3.

[学科分类] 数学（综合）

[关键词] Weak compactness;projectional resolutions;Markushevich bases;Eberlein compacts;Vav sák spaces