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).

Modules Whose Endomorphism Rings are Right Rickart

“…Kaplansky [1] introduced the notion of Baer rings, which was extended to Rickart rings in ([2], [3]), and to quasi-Baer rings in [4], respectively. A number of research papers have been devoted to the study of Baer, quasi-Baer, and Rickart rings (see e.g [1], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]). A ring R is said to be Baer if the right annihilator of any nonempty subset of R is generated by an idempotent as a right ideal of R. The notion of Baer rings was generalized to a module theoretic version and studied in recent years (see [18], [19]).…”

Modules Whose Endomorphism Rings are Baer

“…Kaplansky [1] introduced the notion of Baer rings, which was extended to Rickart rings in ([2], [3]), and to quasi-Baer rings in [4], respectively. A number of research papers have been devoted to the study of Baer, quasi-Baer, and Rickart rings (see e.g [1], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]). A ring R is said to be Baer if the right annihilator of any nonempty subset of R is generated by an idempotent as a right ideal of R. The notion of Baer rings was generalized to a module theoretic version and studied in recent years (see [17], [18]).…”