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Principal quasi-Baerness of formal power series rings

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Abstract

Let R be a ring. We consider left (or right) principal quasi-Baerness of the left skew formal power series ring R[[x; α]] over R where α is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left (or right) principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi-Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.

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References

  1. Liu, Z.: A note on principally quasi-Baer rings. Comm. Algebra, 30, 3885–3890 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Clark, W. E.: Twisted matrix units semigroup algebras. Duke Math. J., 34, 417–423 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  3. Birkenmeier, G. F., Kim, J. Y., Park, J. K.: Principally quasi-Baer rings. Comm. Algebra, 29, 639–660 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Birkenmeier, G. F., Kim, J. Y., Park, J. K.: On polynomial extensions of principally quasi-Baer rings. Kyungpook Math. J., 40, 247–254 (2000)

    MATH  MathSciNet  Google Scholar 

  5. Birkenmeier, G. F., Park, J. K.: Triangular matrix representations of ring extensions. J. Algebra, 265, 457–477 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hirano, Y.: On ordered monoid rings over a quasi-Baer ring. Comm. Algebra, 29, 2089–2095 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hong, C. Y., Kim, N. K., Kwak, T. K.: Ore extensions of Baer and P.P.-rings. J. Pure Appl. Algebra, 151, 215–226 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kaplansky, I.: Rings of Operators, W. A. Benjamin, Inc., New York, 1968

    MATH  Google Scholar 

  9. Birkenmeier, G. F., Kim, J. Y., Park, J. K.: Polynomial extensions of Baer and quasi-Baer rings. J. Pure Appl. Algebra, 159, 25–42 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu, Z.: Triangular matrix representations of rings of generalized power series. Acta Mathematica Sinica, English Series, 22, 989–998 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P. R. China

    Zhong Kui Liu & Wen Hui Zhang

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  1. Zhong Kui Liu
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  2. Wen Hui Zhang
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Correspondence to Zhong Kui Liu.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10961021) and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China

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Liu, Z.K., Zhang, W.H. Principal quasi-Baerness of formal power series rings. Acta. Math. Sin.-English Ser. 26, 2231–2238 (2010). https://doi.org/10.1007/s10114-010-7429-8

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  • DOI: https://doi.org/10.1007/s10114-010-7429-8

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