Resumen de Trivial units for group rings with G-adapted coefficient rings
Yuanlin Li, M. M. Parmenter, Allen Herman
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.
