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

  • Hashemi, Ebrahim ;
  • Moussavi, Ahmad
  • Published : 2004.11.01

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

Baer rings;right p.p.-rings;$\alpha$-rigid rings;skew power eries;Ore extensions

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  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