Differential Extensions of Weakly Principally Quasi-Baer Rings
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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.
KeywordsDifferential polynomial ring Pseudo-differential operator ring Differential inverse power series ring (Weakly) p.q.-Baer APP ring AIP ring s-unital ideal
Mathematics Subject Classification (2010)16D40 16N60 16S90 16S36
The authors would like to express their deep gratitude to the referee for a very careful reading of the article, and many valuable comments, which have greatly improved the presentation of the article.
This research was supported by the Iran National Science Foundation: INSF (No: 95004390).
- 3.Birkenmeier, G.F., Kim, J.Y., Park, J.K.: On quasi-Baer rings. Algebra and Its Applications, 67–92. Contemp. Math., vol. 259. Am. Math. Soc., Providence (2000)Google Scholar
- 29.Paykan, K., Moussavi, A.: Primitivity of skew inverse Laurent series rings and related rings. J. Algebra Appl. https://doi.org/10.1142/S0219498819501160 (2019)