Differential Extensions of Weakly Principally Quasi-Baer Rings
Tóm tắt
A ring R is called weakly principally quasi-Baer or simply (weakly p.q.-Baer) if the right annihilator of a principal right ideal is right s-unital by right semicentral idempotents, which implies that R modulo, the right annihilator of any principal right ideal, is flat. We study the relationship between the weakly p.q.-Baer property of a ring R and those of the differential polynomial extension R[x;δ], the pseudo-differential operator ring R((x− 1;δ)), and also the differential inverse power series extension R[[x− 1;δ]] for any derivation δ of R. Examples to illustrate and delimit the theory are provided.
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