대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권2호
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  • Pages.353-363
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  • 2005
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON (α, δ)-SKEW ARMENDARIZ RINGS

  • MOUSSAVI A. (Department of Mathematics University of Tarbiat Modarres Tehran) ;
  • HASHEMI E. (Department of Mathematics Shahrood University of Technology)
  • 발행 : 2005.02.01
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초록

For a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$, we introduce ($\alpha$, $\delta$)-skew Armendariz rings which are a generalization of $\alpha$-rigid rings and Armendariz rings, and investigate their properties. A semi prime left Goldie ring is $\alpha$-weak Armendariz if and only if it is $\alpha$-rigid. Moreover, we study on the relationship between the Baerness and p.p. property of a ring R and these of the skew polynomial ring R[x; $\alpha$, $\delta$] in case R is ($\alpha$, $\delta$)-skew Armendariz. As a consequence we obtain a generalization of [11], [14] and [16].

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참고문헌

  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. Austral. Math. Soc. 18 (1974), 470-473 https://doi.org/10.1017/S1446788700029190
  3. G. F. Birkenmeier, Jin Yong Kim and Jae Keol Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 24-42
  4. G. F. Birkenmeier, Jin Yong Kim and Jae Keol Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639-660 https://doi.org/10.1081/AGB-100001530
  5. K. R. Gooderl and R. B.Warfield, An introduction to noncommutative Noetherian rings, Cambridge University Press, Cambridge, 1989
  6. E. Hashemi and A. Moussavi, Semiprime skew polynomial rings, submitted
  7. E. Hashemi and A. Moussavi, Skew power series extensions of $\alpha$-rigid p.p.-rigs, Bull. Korean Math. Soc., to appear
  8. Y. Hirano, On the uniqueness of rings of coefficients in skew polynomial rings, Publ. Math. Debrecen, 54 (1999), 489-495
  9. C. Y. Hong, Nam Kyun Kim, Tai Keun Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103-122 https://doi.org/10.1081/AGB-120016752
  10. C. Y. Hong, Nam Kyun Kim, Tai Keun Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), 215-226 https://doi.org/10.1016/S0022-4049(99)00020-1
  11. C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761 https://doi.org/10.1081/AGB-120013179
  12. A. Jategaonkar, Skew polynomial rings over orders in Artinian rings, J. Algebra 21 (1972), 51-59 https://doi.org/10.1016/0021-8693(72)90033-6
  13. I. Kaplansky, Rings of Operators, Benjamin, New York, 1965
  14. N. K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477-488 https://doi.org/10.1006/jabr.1999.8017
  15. J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289-300
  16. Tsiu-Kwen Lee and Tsai-Lien Wong, On Armendariz rings, Houston J. Math. 29 (2003), no. 3, 583-593
  17. M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14-17 https://doi.org/10.3792/pjaa.73.14

피인용 문헌

  1. BAER SPECIAL RINGS AND REVERSIBILITY vol.27, pp.4, 2014, https://doi.org/10.14403/jcms.2014.27.4.531
  2. On Weak Symmetric Rings vol.38, pp.2, 2010, https://doi.org/10.1080/00927870902828702
  3. Nil-Armendariz rings relative to a monoid vol.2, pp.1, 2013, https://doi.org/10.1007/s40065-012-0040-3
  4. The McCoy Condition on Ore Extensions vol.41, pp.1, 2013, https://doi.org/10.1080/00927872.2011.623289
  5. ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS vol.53, pp.2, 2016, https://doi.org/10.4134/JKMS.2016.53.2.381
  6. Armendariz group rings vol.45, pp.7, 2017, https://doi.org/10.1080/00927872.2016.1233341
  7. $$\varvec{\sigma }$$ σ -PBW Extensions of Skew Armendariz Rings 2017, https://doi.org/10.1007/s00006-017-0800-4
  8. On Classical Quotient Rings of Skew Armendariz Rings vol.2007, 2007, https://doi.org/10.1155/2007/61549
  9. Ore Extensions of Skew Armendariz Rings vol.36, pp.2, 2008, https://doi.org/10.1080/00927870701718849
  10. On Rings Having McCoy-Like Conditions vol.40, pp.4, 2012, https://doi.org/10.1080/00927872.2010.548842
  11. A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS vol.81, pp.03, 2010, https://doi.org/10.1017/S0004972709001178
  12. Armendariz modules over skew PBW extensions pp.1532-4125, 2019, https://doi.org/10.1080/00927872.2018.1503281