Baer Group Rings with Involution

Abstract

We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true. Sufficient conditions are given so that for some finite cyclic groups $G$, if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$. We prove that if the group ring $RG$ is a Baer $*$-ring, then so is $RH$ for every subgroup $H$ of $G$. Also, we generalize results of Zhong Yi, Yiqiang Zhou (for (quasi-) Baer rings) and L. Zan, J. Chen (for principally quasi-Baer and principally projective rings).