Abstract
A Ting R with a derivation δ is called δ-semiprime if for any δ-ideal I of R (i.e., an ideal I such that δ(I)⊆ I)I 2 = 0 implies I = 0.R is called δ-quasi-Baer (resp. quasi-Baer) if the right annihilator of every δ-ideal (resp. ideal) of R is generated by an idempotent of R. In this paper, a differential polynomial ring A = R[x;δ] of a ring R with a derivation δ is investigated as follows: For a δ-semiprime ring R, (1) R is δ-quasi-Baer iff A is quasi-Baer iff A is -quasi-Baer for every extended derivation on A of δ (2) R is δ-quasi-Baer iff A is CS-module over a ring A⊗ z A op.
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