Trivial units for group rings with G-adapted coefficient rings

• Autores: Yuanlin Li, M. M. Parmenter, Allen Herman
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 1, 2005, págs. 80-89
• Idioma: inglés
• DOI: 10.4153/cmb-2005-007-1
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• Resumen

  • 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.