Acta Mathematica Vietnamica
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Differential Extensions of Weakly Principally Quasi-Baer Rings
Kamal Paykan
,
Ahmad Moussavi
Abstract
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 $R[x;\delta]$, the pseudo-differential operator ring $R((x^{− 1};\delta))$, and also the differential inverse power series extension $R[[x^{− 1};\delta]]$ for any derivation $\delta$ of $R$. Examples to illustrate and delimit the theory are provided.