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Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 977–991 | Cite as

Differential Extensions of Weakly Principally Quasi-Baer Rings

  • Kamal PaykanEmail author
  • Ahmad Moussavi
Article
  • 80 Downloads

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;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.

Keywords

Differential 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 

Notes

Acknowledgements

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.

Funding Information

This research was supported by the Iran National Science Foundation: INSF (No: 95004390).

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Pure Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran

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