Abstract
AbstractFor each finite groupGfor which the integral group ring ℤGhas only trivial units, we give ring-theoretic conditions for a commutative ringRunder which the group ringRGhas 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 ifRis a ring of finite characteristic andRGhas only trivial units, thenGhas order at most 3.
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