Resumen de Trivial units in abelian group algebras

Peter V. Danchev

• We ¯nd a necessary and su±cient condition when all units in arbitrary abelian group algebras are trivial by reducing it to the torsion case. This is a supplement to our recent results in (Extracta Math., 2008). In particular, we extend theorems due to Ritter- Sehgal (Math. Proc. Royal Irish Acad., 2005) and Herman-Li (Proc. Amer. Math. Soc., 2006).