Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SKEW POWER SERIES EXTENSIONS OF α-RIGID P.P.-RINGS

  • Hashemi, Ebrahim (Department of Mathematics, University of Tarbiat Modarres) ;
  • Moussavi, Ahmad (Department of Mathematics, University of Tarbiat Modarres)
  • Published : 2004.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate skew power series of $\alpha$-rigid p.p.-rings, where $\alpha$ is an endomorphism of a ring R which is not assumed to be surjective. For an $\alpha$-rigid ring R, R[[${\chi};{\alpha}$]] is right p.p., if and only if R[[${\chi},{\chi}^{-1};{\alpha}$]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).

Keywords

References

  1. D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265–2275 https://doi.org/10.1080/00927879808826274
  2. E. P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Aust. Math. Soc. 18 (1974), 470–473
  3. G. F. Birkenmeier, Idempotents and completely semiprime ideals, Comm. Algebra 11 (1983), 567–580
  4. G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639–660
  5. G. F. Birkenmeier, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 24–42
  6. G. F. Birkenmeier, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40 (2000), 247–253
  7. J. A. Fraser and W. K. Nicholson, Reduced PP-rings, Math. Japonica 34 (1989), no. 5, 715–725
  8. Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52
  9. C. Y. Hong, N. K. Kim and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), 215–226
  10. C. Y. Hong, N. K. Kim and T. K. Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103–122
  11. C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751–761
  12. D. A. Jordan, Bijective extension of injective ring endomorphisms, J. London Math. Soc. 35 (1982), no. 2, 435–488
  13. I. Kaplansky, Rings of Operators, Benjamin, New York, 1965
  14. N. H. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477–488
  15. J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289–300
  16. Z. Liu, A note on principally quasi-Baer rings, Comm. Algebra 30 (2002), no. 8, 3885–3890
  17. A. Moussavi and E. Hashemi, Semiprime skew polynomial rings, submitted
  18. M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14–17
  19. C. E. Rickart, Banach algebras with an adjoint operation, Ann. of Math. 47 (1946), 528–550

Cited by

  1. Generalized Quasi-Baer Rings vol.33, pp.7, 2005, https://doi.org/10.1081/AGB-200063514
  2. Baer and Quasi-Baer Properties of Skew Generalized Power Series Rings vol.44, pp.4, 2016, https://doi.org/10.1080/00927872.2015.1027370
  3. Principally Quasi-Baer Skew Power Series Modules vol.41, pp.4, 2013, https://doi.org/10.1080/00927872.2011.615357
  4. On principally quasi-Baer skew power series rings 2015, https://doi.org/10.1142/S1793557115500084
  5. Principally Quasi-Baer Skew Power Series Rings vol.38, pp.6, 2010, https://doi.org/10.1080/00927870903045173
  6. Principally Quasi-Baer skew Generalized Power Series modules vol.42, pp.4, 2014, https://doi.org/10.1080/00927872.2012.738338
  7. Skew power series extensions of principally quasi-Baer rings vol.45, pp.4, 2008, https://doi.org/10.1556/SScMath.2008.1071