Skew polynomial rings over σ-quasi-Baer and σ-principally quasi-Baer rings

Let R be a ring R and sigma be an endomorphism of R. R is called sigma-rigid (resp. reduced) if asigma(a) = 0 (resp. a(2) = 0) for any a is an element of R implies a = 0. An ideal I of R is called a sigma-ideal if sigma(I) subset of or equal to I. R is called sigma-quasi-Baer (resp. right (or left) sigma-p.q.-Baer) if the right annihilator of every sigma-ideal (resp. right (or left.) principal sigma-ideal) of R is generated by an idempotent of R. In this paper, a skew polynomial ring A = R[x; sigma] of a ring R is investigated as follows: For a sigma-rigid ring R, (1) R is sigma-quasi-Baer if and only if A is quasi-Baer if and only if A is sigma-quasi-Baer for every extended endomorphism sigma on A of sigma; (2) R is right sigma-p.q.-Baer if and only if R is sigma-p.q.-Baer if and only if A is right sigma-p.q.-Baer if and only if A is p.q.-Baer if and only if A is sigma-p.q.-Baer if and only if A is right sigma-p.q.-Baer for every extended endomorphisin or on A of sigma.