Abstract :
The maximal symmetric ring of quotientsQσ(R), as defined by Utumi, is a symmetric version of the maximal ring of quotients ofR. For the most part, we study this ring whenR=K[G] is a group algebra. For example, we show that ifGis a free product of groups and ifR=K[G] is a domain, thenQσ(R) is usually equal toR. On the other hand, there are certainly groups for whichQσ(R) is properly larger thanRand we construct a number of such examples.
