ON STRICTLY GENERALIZED P-QUASI-BAER RINGS

Banh Duc Dung; Truong Cong Quynh; Le Duc Thoang

Banh Duc Dung
Truong Cong Quynh
Le Duc Thoang

Keywords: PP ring, (strictly)generalized PP ring, p-quasi-Baer ring, (strictly) Gpquasi-Baer ring, von Neumann regular ring

Abstract

A ringR is called strictly generalized right p-quasi-Baer if for any nonzero element x ∈ R, there exists a positive integer n such that xn =0 and the right annihilator of xnR is generated by an idempotent. The class of strictly right generalized right p-quasi-Baer rings is a new class of generalized right p-quasi-Baer rings and contains right principally quasiBaer rings. In this paper, many properties of these rings and relations to another kinds of rings are studied, the closeness of this class of rings and some relative classes under direct products or direct sums is investigated.