Resumen de Trivial units in commutative group algebras

Peter V. Danchev

• Let G be an arbitrary abelian group and let R be a commutative unitary ring of arbitrary characteristic. A necessary and su±cient condition is given for when all units in the group ring RG are trivial provided that either supp(G) \ inv(R) 6= ; or RG is modular.

  In particular, we establish a comprehensive characterization by ¯nding a criterion when RG has only trivial units provided that char(R) is a positive number greater than 1. These achievements strengthen results due to Karpilovsky (Arch. Math. Basel, 1983), Herman-Li- Parmenter (Can. Math. Bull., 2005) and the author (Math. Commun., 2005).