Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 33 No. 2 (2015): Revista Integración
Research and Innovation Articles

Skew PBW Extensions of Baer, quasi-Baer, p.p. and p.q.-rings

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  • Armando Reyes
Armando Reyes
Universidad Nacional de Colombia
DOI: https://doi.org/10.18273/revint.v33n2-2015007

Published 2015-12-04

Keywords

  • Baer,
  • quasi-Baer,
  • p.p. and p.q.-Baer rings,
  • skew Poincaré-Birkhoff-Witt extensions.

How to Cite

Reyes, A. (2015). Skew PBW Extensions of Baer, quasi-Baer, p.p. and p.q.-rings. Revista Integración, Temas De matemáticas, 33(2), 173–189. https://doi.org/10.18273/revint.v33n2-2015007

Abstract

The aim of this paper is to study skew Poincaré-Birkhoff-Witt extensions of Baer, quasi-Baer, p.p. and p.q.-Baer rings. Using a notion of rigidness, we prove that these properties are stable over this kind of extensions.

To cite this article: A. Reyes, Skew PBW Extensions of Bear, quasi-Baer, p.p. and p.q.-rings, Rev. Integr. Temas Mat. 33 (2015), No. 2, 173–189.

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References

  1. Armendariz E.P., “A note on extensions of Baer and p.p.-rings”, J. Austral. Math. Soc. 18 (1974), 470–473.
  2. Armendariz E.P., Koo H.K. and Park J.K., “Isomorphic Ore extensions”, Comm. Algebra 15 (1987), No. 12, 2633–2652.
  3. Birkenmeier G.F., “Baer rings and quasicontinuous rings have a MDSN”, Pacific J. Math. 97 (1981), No. 2, 283–292.
  4. Birkenmeier G.F., Kim J.Y. and Park J.K., “Principally quasi-Baer rings”, Comm. Algebra 29 (2001), No. 2, 639–660.
  5. Birkenmeier G.F., Kim J.Y. and Park J.K., “Polynomial extensions of Baer and quasi-Baer rings”, J. Pure Appl. Algebra 159 (2001), No. 1, 25–42.
  6. Clark W.E., “Twisted matrix units semigroup algebras”, Duke Math. J. 34 (1967), 417–423.
  7. Gallego C. and Lezama O., “Gröbner bases for ideals of σ-PBW extensions”, Comm. Algebra 39 (2011), No. 1, 50–75.
  8. Han J., Hirano Y. and Kim H., “Semiprime Ore extensions”, Comm. Algebra 28 (2000), No. 8, 3795–3801.
  9. Han J., Hirano Y. and Kim H., “Some results on skew polynomial rings over a reduced ring”, in International Symposium on Ring Theory (Kyongju, 1999), Trends Math., Birkhäuser Boston, Boston, MA (2001), 123–129.
  10. Hashemi E., Moussavi A. and Seyyed Javadi H.H., “Polynomial Ore extensions of Baer and p.p.-rings”, Bull. Iranian Math. Soc. 29 (2003), No. 2, 65–86.
  11. Hashemi E. and Moussavi A., “Polynomial extensions of quasi-Baer rings”, Acta Math. Hungar. 107 (2005), No. 3, 207–224.
  12. Hinchcliffe O., “Difussion Algebras”, Thesis (Ph.D.), University of Sheffield, Sheffield, 2005, 118 p.
  13. Hong C.Y., Kim N.K. and Kwak T.K., “Ore extensions of Baer and p.p.-rings”, J. Pure Appl. Algebra 151 (2000), No. 3, 215–226.
  14. Hong C.Y., Kim N.K. and Lee Y., “Ore extensions of quasi-Baer rings”, Comm. Algebra 37 (2009), No. 6, 2030–2039.
  15. Kaplansky I., Rings of Operators. W.A. Benjamin, Inc., New York-Amsterdam, 1968.
  16. Krempa J., “Some Examples of reduced rings”, Algebra Colloq. 3 (1996), No. 4, 289–300.
  17. Lezama O. and Reyes A., “Some homological properties of skew PBW extensions”, Comm. Algebra 42 (2014), No. 3, 1200–1230.
  18. Lezama O., Acosta J.P. and Reyes A., “Prime ideals of skew PBW extensions”, Rev. Un. Mat. Argentina 56 (2015), No. 2, 39–55.
  19. Matczuk J., “A Characterization of σ-rigid rings”, Comm. Algebra 32 (2004), No. 11, 4333–4336.
  20. McConnell J.C. and Robson J.C., Noncommutative Noetherian rings, Graduate Studies in Mathematics, 30, American Mathematical Society, Providence, RI, 2001.
  21. Nasr-Isfahani A.R. and Moussavi A., “Baer and quasi-Baer differential polynomial rings”, Comm. Algebra 36 (2008), No. 9, 3533–3542.
  22. Passman D.S., “Prime ideals in enveloping rings”, Trans. Amer. Math. Soc. 302 (1987), No. 2, 535–560.
  23. Reyes A., “Ring and module theoretical properties of skew PBW extensions”, Thesis (Ph.D.), Universidad Nacional de Colombia, Bogotá, 2013, 142 p.
  24. Reyes A., “Jacobson’s conjecture and skew PBW extensions”, Rev. Integr. Temas Mat. 32 (2014), No. 2, 139 -152.