Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 32 No. 2 (2014): Revista Integración, temas de matemáticas
Research and Innovation Articles

Jacobson’s conjecture and skew PBW extensions

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  • Armando Reyes
Armando Reyes
Universidad Nacional de Colombia

Published 2014-11-04

Keywords

  • Noncommutative rings,
  • Jacobson’s radical,
  • skew PBW extensions

How to Cite

Reyes, A. (2014). Jacobson’s conjecture and skew PBW extensions. Revista Integración, Temas De matemáticas, 32(2), 139–152. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4389

Abstract

The aim of this paper is to compute the Jacobson’s radical of skew PBW extensions over domains. As a consequence of this result we obtain a direct relation between these extensions and the Jacobson’s conjecture, which implies that skew PBW extensions over domains satisfy this conjecture.

To cite this article: A. Reyes, Jacobson’s conjecture and skew PBW extensions, Rev. Integr. Temas Mat.32 (2014), no. 2, 139-152.

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References

  1. Cauchon G., “Sur l’intersection des puissances du radical d’un T -anneau noethérien”, C. R. Acad. Sci. Paris Sér. A 279 (1974), 91-93.
  2. Cauchon G., “Les T-anneaux, la condition (H) de Gabriel et ses consequences”, Comm. Algebra 4 (1976), no. 1, 11-50.
  3. Gallego C. and Lezama O., “Gröbner bases for ideals of σ − PBW extensions”, Comm.Algebra 39 (2011), no. 1, 50-75.
  4. Goodearl K.R. and Warfield R.B. Jr., An introduction to noncommutative Noetherian rings, Second edition. London Mathematical Society Student Texts, 61, Cambridge University
  5. Press, Cambridge, 2004.
  6. Herstein I.N., “A counterexample in Noetherian rings”, Proc. Nat. Acad. Sci. 54 (1965), 1036-1037.
  7. Hinchclife O.G., Diffusion Algebras, Thesis (PhD), University of Sheffield, Sheffield, 2005,119 p.
  8. Jacobson N., “The radical and semi-simplicity for arbitrary rings”, Amer. J. Math. 67 (1945), 300-320.
  9. Jacobson N., “Structure of rings”, in American Mathematical Society, Colloquium Publications, vol. 37, AMS 190, Hope Street, Prov., R.I., 1956, 263 p.
  10. Jategaonkar A.V., “Left principal ideal domains”, J. Algebra 8 (1968), 148-155.
  11. Jategaonkar A.V., “A counter-example in ring theory and homological algebra”, J. Algebra 12 (1969), 418-440.
  12. Jategaonkar A.V., “Jacobson’s conjecture and modules over fully bounded Noetherian rings”, J. Algebra 30 (1974), 103-121.
  13. Jategaonkar A.V., “Noetherian bimodules”, in Proceedings of the Conference on Noetherian Rings and Rings with Polynomial Identities, University of Leeds (1979), 158-169.
  14. Jategaonkar A.V., “Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension”, Comm. Algebra 10 (1982), no. 1, 19-69.
  15. Kaplansky I., Commutative rings, Allyn and Bacon, Boston, 1970.
  16. Lam, T.Y., A First Course in Noncommutative Rings, Second edition, Grad. Texts in Math. 131, Springer-Verlag, New York, 2001.
  17. Lenagan T.H., “Noetherian rings with Krull dimension one”, J. Lond. Math. Soc. (2) 15 (1977), no. 1, 41-47.
  18. Lezama O. and Reyes A., “Some homological properties of skew PBW extensions”, Comm. Algebra 42 (2014), no. 3, 1200-1230.
  19. McConnell J.C. and Robson J.C., Noncommutative Noetherian Rings, Grad. Studies in Math. 30, AMS, 2001.
  20. Reyes A., “Ring and module theoretic properties of skew PBW extensions”, Thesis (Ph.D.), Universidad Nacional de Colombia, Bogotá, 2013, 142 p.
  21. Rosenberg A.L., “Noncommutative algebraic geometry and representations of quantized algebras”, in Mathematics and its Applications 330, Kluwer Academic Publishers Group,
  22. Dordrecht, 1995.
  23. Schelter W., “Essential extensions and intersection theorems”, Proc. Amer. Math. Soc. 53
  24. (1975), no. 2, 328-330.