Baer Group Rings with Involution

Year 2017, , 1 - 10, 11.07.2017

Anil Khairnar B. N. Waphare

https://doi.org/10.24330/ieja.325913

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).

Keywords

Group ring, Baer $*$-ring

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